Just wanted to clarify for RichRaven:
The CCCs we have mentioned have preapproval sites where you can enter your information and see what cards you may be preapproved or prequalified for. I just noticed that the subject line of your thread says "Where to apply for a credit card without a hard pull." You cannot apply for any credit card without a hard pull (with the exception of Crown Jewelers, but you don't want that because I know you already have positive accounts reporting).
Keep in mind that even if you have a preapproval, an approval is not guaranteed. It is still entirely possible to be declined even after you get a preapproval from one of these CCCs. Also, even if you have a preapproval, they will still pull a hard inquiry when you actually apply.