You should definitely check out the Hiroshima Peace Park where the Atomic Bomb Dome and the Peace Memorial Museum are located. I think you could spend an entire morning here. After that, you can proceed to downtown Hiroshima to try the Hiroshima Okonomiyaki - it's one of the specialities of Hiroshima, so definitely a must try! If you have time, you could check out the Hiroshima castle which is very close to the town centre.
On your 2nd day, you could take a day trip to Miyajima which is famous for its giant torii gate. You could spend an entire day here just exploring the shrines or take a walking trail up to Mt Misen on Miyajima. It's just a short ferry ride away from Hiroshima.
I agree with the other posts. When I visited Hiroshima I had one relaxed day looking at the Peace Memorial Park area and it's better to slow down and take it all in here then rush through it.
The second day I spent at Miyajima, fending off the deer, hiking up the mountain and wandering through the shrine and it was a great day.
You could also go to Rabbit Island if you like Rabbits.