Having a bank would be nice. But if there was one there would have to be incentives to put money in. Like having to deal with thieves, and pickpockets.
Banks need to be guarded.
The best banks need giants as security, and maybe a dragon on the roof or in the main vault.
There also needs to be a way to equip your character such that before he robs the bank, he can wear armor that is the spittin' image of Clint Eastwood's apparel in "For A Few Dollars More."
(And for those of you who've never seen the film - your life is empty and without substance. Seriously.)