That is quite the change, good for you. I think about the settlers who moved west across the Mississippi, the balls that took, just pack up your horse maybe a cart and start over... Pretty cool...
As far as banks go, I use 3 banks and none of them are breaking any records in customer service. I use an international bank, then BOA, and a local credit union. The truth of the matter is, if you don't have any loans and you are just looking for a checking/savings account with a debit card, then use Bank of America or something comparable, I can go anywhere in the country and get money with just my pass word and a finger print, I can have people 30 states away walk in a branch with my account number and deposit cash into my account. Its just more convenient and easier...
Do not use them for loans but for save/check they aren't that bad to deal with, you should really never have to deal with them except for starting the account which is easy.. If you are going for a loan go to a local credit union or AAA...
So if you are not sure of where you will be next, use a bank that is everywhere, if you are all settled in and never plan on moving, then use a small local bank where you get better CS. I used a local bank for all of my work related stuff, payroll accounts and small business checking. If your life isn't that confusing then BOA should be fine, don't get me wrong they suck when it comes to loans and dealing with anything out of the ordinary, but their online banking is very easy to use, they are everywhere, and they are not going anywhere...
For example - I recently went from 11 bank accounts to maintain down to 4, closing the local accounts was simple and painless, closing the national accounts turned into a headache and they were still sending me zero balance statements because they said they had to leave one of the accounts open for 90 days incase there are other debits out, but if you have a zero balance in the account and it is open they charge you a monthly service fee, which I didn't know, so if my office manager didn't catch it I would have paid them fees and probably $70 a month in over drafts since there was nothing in there, so she had to transfer {which because the other accounts were no longer linked to it had to be hand deposited} $500 into the account and then after 90 days they will send me the $500 back when the accounts are closed...
Luckily I have someone to deal with all of that, she just vented to me what a PITA it was and all I had to do was listen, but if I had to deal with it I would have been pulling my hair out screaming into a phone for 4 hours...
Anyway, good luck with the move, I hope everything turns out well and you find what you are looking for...