Vietcombank
Add: 54D Hung Vuong
Offers the usual kinds of services, such as exchanging travellers cheques, and has an ATM.

There's another handy branch
Add: Hotel Saigon Morin - 30D Le Loi
Opened: 7am - 10pm; Mon - Sat.

Industrial and development bank
Add: 41D Hung Vuong
Which has the same service.