Hana Hostel is just a short walk from the station (between the station and Mazda Stadium). They have typical hostel rooms (where strangers may share the same room) as well as private rooms. I stayed in a private room, which was Japanese-style. The futons were very comfortable. The room has a small TV, air conditioner, outlets, and they also offer internet access, although I didn't bring a laptop.
There is a computer in the entrance that anyone may use. They also have brochures for various places in the area and beyond and they keep track of when the local baseball team, the Carps, have home games, which makes it easy to go to a game if you are here when they're playing. You can walk to the stadium from the hostel.
On the top floor the have washing machines/dryers. The dryers worked well, although you can also hang your clothes if you wish.
The staff here is helpful and friendly. It's a nice place to stay for those in Hiroshima on a budget.
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