Best free bank account and credit card with benefits (no annual fee)?

I'm currently living in Boston and I have a Bank of America bank account and Visa. I recently discovered that they charged me a monthly fee (first they they ever charged me that). Now, BoA told me that I can avoid the fee going forward if I convert my account into an online account. I said I'll think about it. I'm thinking of keeping the account and going with another institution to keep things as flexible as possible. Is this a good idea? Does anyone here have any recommendations for a financial institution that doesn't have minimum or very low minimum account balances to avoid fees?

Also, I'm using a basic BoA Visa card. I have a credit limit of $3000. I got this card long before the financial crisis began and I've been good. I never paid interest or had late payments. I'm thinking of going with something else that offers points or rewards. Someone told me to go with the Amazon.com Rewards Visa since I use them a lot. However, I also fly at least 3 times a year. I'm not sure if there are good, but free credit cards with reward miles. I'm currently back in school and my annual income is about $15,000. I spend between $3000-$4000 on my card on an annual basis. Any suggestions for a card with decent benefits that have no annual fees?

Thanks!