I recommend Bank of America. I switched to them over 20 years ago from a small bank and have no regrets. I've got two checking and one savings account, a line of credit, Visa card and a mortgage with them (because they bought Countrywide). All of these accounts are online and it is so simple. In Houston, BOA ATMs are everywhere. I don't want "personal service". I don't want the tellers to recognize me because I only go to a branch about once every 2 or 3 years. When you combine BOA with Quicken, banking doesn't get any better IMO. All the information you want is at your fingertips with very little effort.
I have a savings account separate from my checking account because, well, it's a savings account I don't want to touch unless it's an emergency. I auto transfer $x from my checking account to my savings account twice a month. Any spending money or other day-to-day spending comes from my checking account while my savings account accrues money and a bit of interest without me worrying about it. The interest rates are so low nowadays, there's no point in doing it for that alone.
And with the low rates, that's why earning interest isn't a deciding factor. At one point a couple of years ago I had "spending money" in my checking, savings (earning pennies in interest) and short term CDs since I thought it was a neat idea at the time. But the CDs also earned very little and were a pain in the ass to transfer back into savings (the credit union loved to rollover and renew the CD, thus locking it up and threatening a penalty if I needed to access it). It wasn't as malicious as it sounds, just annoying. I never really needed to access the CD, but when it came to paying rent, I always wanted to keep a cushion in my checking while replenishing the savings. And with rates so low there's no reason for me to pursue a CD any time soon, especially without a substantial amount to invest. But having the savings with the checking has a good effect of paying closer attention to account balances. It's silly and psychological, but that's the only reason for separate savings/checking at this point. And BOA would be great if I were in Texas (or anywhere else that actually had BOAs, but not where I am at the moment).