Cobranded would typically offer the best bang for the buck with status and rewards if you were looking to build them up for personal use.
If you are looking for a brand-agnostic card and you are purchasing your own stays and being reimbursed, there could be a lot of earnings through things like Amex Travel and Chase Travel. Suggestions would really depend on how you plan to redeem the rewards, though, and if toward flights in which cabin, which alliance, and which origins/destinations.
I'm assuming your travel is primarily by car since you're focused on hotel and not hotels/flights? That makes a difference. And also, do you purchase airfare for personal travel such as vacations? Some cards have a better redemption value for airfare.
As others have said, brand-specific cards may offer better overall value if they will work for your situation. The major hotel chains listed above offer a large footprint with properties in many markets and at varying price-points. If you decide to stick with one chain, getting a card that offers an annual "free night" benefit will normally offset the annual fees and you'll get superior earnings for purchases in the hotel, to include things such as restaurant bills charged to your room. If you are unable or unwilling to use any card's benefits and credits against the AF, then that's a poor card-match for you. If the card is a good fit, the AF often becomes a moot point.
Since others have discussed more about the hotel-branded cards, I'll go over some of the best general purpose travel cards available today. If you truly need a brand-agnostic card, there are plenty to choose from that could work reasonably well. For some, you will still get better redemption value of rewards if you use them for travel. Some suggestions:
Chase Sapphire Preferred Visa: AF $95 but offset with a $50 credit against hotel purchases though Chase. (Effective AF $45.) Earns Chase Ultimate Rewards points (URs.) 1 point always = at least 1% in cash value, so URs can be a better value for cash redemption options than some competing point cards. 5x points on travel purchased through Chase. Also, through 03/2022, 5x points on LYFT. 3x points on dining out. 3x points on online grocery purchases. 3x points on streaming services. 2x points on all travel purchased outside of Chase. Points are worth 25% more in value when redeemed for travel through the Chase portal. No Foreign Transaction Fee. Ability to transfer points 1:1 value to airline and hotel partners including United, Southwest or Jet Blue airlines plus international partners; Marriott, Hyatt, and IHG hotels. Benefits with Door Dash and Pelaton. Travel and purchase protections including primary Rental Car CDW. Current SUB is 100K UR points (on $4k spend) worth up to $1,250 in value when redeemed through Chase travel.
*Note: I personally like the Chase Sapphire Reserve Visa but the CSP is an overall better value for many AF-averse travelers. CSR has a higher $550 AF with $300 in travel credits, making the effective AF $150. CSR magnifies UR point redemption by 50% instead of 25% for CSP. There are additional credits than can further lower the fee and it offers other premium Visa Infinite benefits not available on CSP, but CSP can be easier to justify for many of our members, especially after the recent Chase "refresh" of the card.
Citi Premier Mastercard: AF $95 but easily offset by annual hotel credit of $100 for one stay of $500 of more. (If your business travel costs less per stay, it could be used on a personal vacation.) Earns Citi Thank You points (TY.) 3x points for air travel, hotels, restaurants, grocery stores, gas stations. Ability to transfer points to airline partners at a higher value; gift card/cash redemption may be 1 ccp or less. Citi currently offers no hotel partners for point transfer. No Foreign Transaction Fee. Current SUB is 80K TY points (on $4K spend) worth $800 in gift cards.
American Express Green charge card: For someone who purchases less airfare, this may be a less desirable selection for you that the two cards above. AF $150 with credits that are more useful for air travel ($100 credit for CLEAR security for airports and stadiums; $100 credit for airport lounges.) Earns AMEX Member Rewards points (MRs.) 3x MR on travel including hotels, 3x points on transit, 3x points on restaurants. No Foreign Transaction Fees. Ability to transfer points to airline/hotel partners at 1:1 value including Delta, Hawaiian, Jet Blue airlines plus international partners; and Marriott, Hilton, and IHG hotels. Like Citi TY points, MR gift card/cash values may be 1 ccp or less. While the transfer partners are better than Citi Premier, if you can't claim the $200 in airline-related credits the $150 AF may be more burdensome that the Premier for less frequent fliers. Current SUB is 45K MR points (on $2K spend.)
Bank of America Premium Rewards Visa: *Mainly a contender if you can move assets including IRA accounts of at least $50K to $100K into Merrill Lynch/Bank of America to qualify for the Platinum Honors level of their Preferred Rewards. AF of $95 can be completely offset by $100 annual airline fee credit as well as $100/4 years TSA Global Entry credit. Base earnings are 1.5% on everything and 2% on all dining and travel. However, with Preferred Rewards status of Gold/Platinum/Platinum honors, the earning are multiplied by 1.25, 1.50 or 1.75. So the top rate earns 3.5% in cash value on all travel and dining plus 2.625% on everything else. At the "Platinum" level ($50K invested), the earnings are still a very respectable 3% for dining/travel and 2.25% everything else. (One benefit is this card earns straight-forward cash value redemption. The value of any points-based system may change or become diluted; value can't be determined until they are redeemed.) No Foreign Transaction Fees. Travel and purchase protections. Current SUB 50K points (on $3K spend) worth $500.
US Bank Altitude Reserve Visa: *You need to be an established customer of USB with either deposit accounts or another credit card to be approved for the AR. AF $400 but card has $325 in travel credits against the AF, making the effective AF $75. Earns 5x points on prepaid hotels and car rentals booked through USB. 3x points on all mobile wallet purchases (Apple Pay, Google Pay, Samsung Pay, etc.) 3x points on travel. Premium Visa Infinite benefits. No Foreign Transaction Fee. Redemption through Real-Time Rewards (RTR) can be worth 50% more in value. Current SUB is 50K points (on $4500 spend) worth up to $750 in travel.
Navy Federal Credit Union Flagship Rewards Visa: $49 AF but has TSA Global Entry credit for $100/4 years making effective AF $24 if you travel internationally. Earns 3X points on travel and 2X points on everything else. Points can be redeemed for cash at 1 ccp or for travel purchases though the travel portal. Not only No Foreign Transaction Fee but also no Cash Advance or Balance Transfer fees. APR as low as 9.99%, much lower than other travel cards. Includes travel accident insurance, cell phone protection, and travel and emergency assistance. Current SUB is 40K points (on $4K spend) worth $400 plus one year of Amazon Prime worth $130. Caveats: Minimum redemption of $50 is higher than many cards. Also, while you don't need to be a veteran to join, if you aren't a veteran you must have a family member who was including parents, grandparents, children, or siblings.
Citi Costco Cash back Visa: No AF beyond basic Costco membership. 
A great value if you already shop in the warehouse! Earns 4% cash back on gasoline (up to $7K annually.) Earns 3% on travel and dining, uncapped. 2% at Costco/Costco.com. No Foreign Transaction Fee. Caveat: Rewards are paid annually in a check that must be redeemed inside a Costco warehouse.
If you are a veteran and can qualify for the PenFed Honors Advanatage program, the PenFed Pathfinder Rewards Visa is definitely worth a look. The $95 AF is waived for Honors Advantage members. Credits include $100 annual airline fee credit and $100/4 years TSA Global Entry credit. Beside the AF waiver, the card earns a higher 4x points on travel for Honors Advantage members ... or 3x points for other members. (Travel includes airfare, hotels, car rentals, cruises, travel agencies, tolls, commuter transportation, Bus lines, Taxi/Uber/Lyft.) Earns 1.5X points on all non-travel purchases. Points are worth no less than 00.85 ccp but up to 1 ccp when redeemed for travel. No Foreign Transaction Fees or Cash Advance fees. Minimum redemption is 1K points. Unlike most of the above cards whose points do not expire as long as the account is open and in good standing, the Pathfinder Rewards points expire FIVE (5) years after being awarded. Current SUB 50K points (on $3K spend) worth up to $500.
My other suggestion would be a simple flat-rate card. The top pick would be the AOD FCU Visa Signature, which offers a flat 3% uncategorized and uncapped cash back. The application process is a little difficult but the card is exceptional. No AF. Rewards are automatically credited monthly against the statement balance. Very low 7.49% APR. No Foreign Transaction Fee. No balance transfer fee. Low cash advance fees. Balance transfers and cash advances process at the same APR as purchase APR, as low as 7.49%.
Yes, the Citi Custom Cash Mastercard could be used for 5% back on up to $500 monthly on hotels*. ($25 monthly maximum in rewards value.) If you only spend on-average of $125 per week or less on hotels and you don't use the card for other categories, it could be a good fit. However, the dismal 1% earnings over any spending over $500 in highest category or for secondary categories might easily wipe out your higher 5% rewards if you don't monitor spending or use other cards as part of your program. That is why some of the above cards might be a better suggestion for you, depending on your spending and alternative card options. The Custom Cash has a lower but easier to reach SUB at $200 for $750 in spending. While the Custom Cash has no AF, it also includes a 3% FTF, so it's not a thrifty pick for international purchases.
*One Custom Cash category is "Select Travel" defined as "Includes airline, hotel, cruise line and travel agency purchases. Excludes timeshares, boat leases and rentals, campgrounds and trailer parks, and real estate agencies."
