Closed cards will continue to show on your credit reports up to 10 years, so you won't see any score drops due to account ages from closing accounts, at least not right away. By the time they've dropped off, the accounts you've kept open will also have aged 10 years.
Your total available credit will drop, which can impact scores by making utilization go up if you have balances reporting.
With no annual fee cards, it's up to you. I could see closing cards you know you'll never use again, like Mattress Firm, but maybe close them gradually, like one every 3 months or something. Start with the lowest limits or the cards you're least likely to use again. That way you don't have multiple accounts dropping off your reports at the same time in 10 years or so. Also, if you close several at once, and someone reviews your report (either when applying for new credit, or in an account review), they might wonder why you closed so many at once.
As I have said (too many times!) when this topic comes up: IMO the problem is that the advantages and disadvantages on each side are very SMALL, and this seems to generate all the heat that comes up in the discussion.
I classify the positions as:
1) Keep what doesn't do (much) harm. No AF, continues to age adding to AAoA and thus score, adds to total CL helping util (very minor for typical starter store cards), might need one day (move, sudden need for item) or "bad" card could improve and become useful.
2) Drop what isn't useful: Too much work (and loss of rewards on better cards) to keep lots of useless cards alive, increase in potential fraud risk (have to periodically check unused accounts), too much "clutter", some concerns about toy cards looking bad on CR
Again, most or all of this is small, each a non-issue to different people. And I guess that's to be expected: if there was an obvious reason, e.g. having the Barclays Uber guarantees happiness, there wouldn't be so much discussion.