I have a Citi credit card and I *had* a Citi bank account until this past week. I opened my account almost 10 years ago and enjoyed some good benefits (ThankYou points, which could be converted to cash for online bill pay, etc.). However, over the past year, Citibank has really declined and is now sticking it to customers. ThankYou points for banking are no longer available unless you have high balances in your account or have an upper tier (e.g., high balance or other requirements) account or if you in some other way give Citibank your money (give--as in NEVER get it back--through fees). Also, it is difficult to avoid montly fees for banking unless you meet the balance requirements or have direct deposit AND online bill pay activity each month. I say NO THANK YOU to Citibank. I closed my account.
I still have a Citi credit card. It's not that great, so I don't use it often. They DO now offer a new credit card that gives you 2% cash back (Double Cash card, I think is what it's called). That's a pretty good deal compared to other cards out there, but any time you open a new credit card, it hits your credit report/score negatively, so I tend to only open a card when the deal is spectacular (I'm still considering the Double Cash card, but it is not compelling enough for me to act yet).
Back to banking: I recommend looking into a local credit union if you want to be able to bank and not pay excessive fees. Most credit unions offer a MUCH better deal than the banks do now.