Deutsche Bank is probably the most expansive one. Sparkasse are also nation wide. Only advantage with Deutsche Bank is that you can withdraw money for free at atms of the follwing banks
Bank Of America,USA
Barclays, UK
BNP Paribas, France
Scotiabank, Canada
Westpac, Australia
TEB, Turkey
My Sparkasse charges me 6€ if I use the debit card overseas which is in my opinion okay.
Eppendorf is a very nice area of Hamburg. The most popular, hip and trendy area is at the moment the Schanzenviertel.