I am with AbuDhabi Commercial Bank (ADCB) and quiet happy with it. Pretty much all the banks in Dubai are going to rip you off with their hidden fees. Make sure you find out the following:
1.Number of times you can use ATM. (There are extra hidden charges sometimes)
2.Number of times you can use the Teller.
3.Online banking fees
4.Minumum amount you must maintain in your account before they start ripping you off!
Good luck.