C.S.
I don't think there is a bank that doesn't offer online banking so you have a lot of options!
I loved banking with Citibank-we didn't have one locally so i did everything online-never once stepped inside a branch. We wanted to consolidate everything though so we went with US bank. I like them a lot and again, they are local to us, but maybe 2 times a year I need to actually go in to a branch.
I would avoid M&I and Chase-in my experience-online or in person they aren't very consumer focused-unless you are one of their 'big spenders'.