If you choose wisely, where you move in the country doesn't matter. For example, I've been with Alliant CU since 2011 for Savings and 2014 for Checking (which pays 0.65% APY btw). They're based out of Chicago and have very minimal brick-and-mortar presence (i.e., not that many physical branch locations, allowing them to pass on savings to customers in the form of very high savings rates). I've never once been to their physical location(s).
I recommend a hybrid approach based on needs:
- Choose a good FI (financial institution, includes banks and CUs (credit unions)) that offers free checking with no hoops to jump through. Bonus points if it also has competitive savings, ATM fee rebates, good online banking, etc. I've been ecstatic with Alliant CU and highly recommend them.
- Only supplement with a local FI if you could benefit from local services. For example, if you need a safe deposit box (SDB), you would need a local FI that has them available. If you need free notary public services, a local FI presence could help. If you need to deposit a ton of coins, a local FI presence could help.
I basically do all my banking online and have zero need to ever visit a physical location anymore. I recommend steering clear of the big FIs like Citi, Chase, BoA, Wells Fargo, PNC, etc. since they've come to nickle and dime the customer with fees and BS and have
terrible savings rates.
Go with a national FI with a good reputation, such as USAA, Navy Federal CU, Digital Federal CU, Pentagon Federal CU, Alliant CU, etc. Others on the Web love Ally, but I had a horrendous experience with them in 2013 trying to open savings, then subsequent savings accounts, and their customer service was dishonest and infuriating, so I recommend against Ally based on my experience alone. I'm a member of all of the above (except Ally) for different reasons, but their savings rates suck except for DCU's APY on the first $1000. Very happy with Alliant CU for checking and savings (with like 10 supplemental savings accounts -- one for each goal -- for Emergency fund, Vacation, Wedding, Next Vehicle, etc.)
Bottom line in all this is that where you go to med school, residency, or eventually end up living and working should no longer be relevant to where you bank, since all the important services are done via online banking, mobile banking, and EFT/ACH anyways, with decreasing reliance on a local brick-and-mortar presence.