1. Will closing these accounts hurt my credit score.
Unlikely, though a new bank might do a credit check that could ding your score a tiny bit. A bank account isn't a credit account, so an account closure shouldn't affect your score unless you close a credit line along with it.
2. Any pitfalls you see to the approach other than going completely online.
Besides the ATMs, I know that Capital One 360 limits the number of transfers between accounts per month. For example, if I want to send money via a friend's Capital One 360 account, or if I want to transfer money from one sub-account to another. This shouldn't affect checks or anything, so it's really not a big deal.
It might be good to keep your credit union account since it's so old.
3. Any advice you'd have or recommended banks.
Capital One 360 is decent. It used to be ING, and it hasn't changed significantly since.
I don't usually care about my bank's rates. I use a zero-interest checking account and move excess money into Vanguard at a regular basis.