Gosh this makes me miss Japan.
For dinner, Hiroshima style Okonomiyaki is my favorite food of all time.
If it's baseball season, definitely catch a Carps game. The energy around Japanese baseball is DIFFERENT. Tickets can be hard to find, but if you plan far enough in advance, can maybe buy some online. This might be tough because when I did this, they mailed the tickets, so might need a Japanese address to mail these to. The baseball stadium is walkable from Hiroshima station.
If you want the history, Hiroshima peace memorial Park, the atomic bomb dome, and the museum. Very well done and somber museum about the atomic bomb from the Japanese point of view. Think Holocaust museum. Can easily take up a full morning or afternoon. When I took my wife to Hiroshima for the first time, this was a must. One stop down from Hiroshima station, but maybe a 30-45 minute walk instead if it's a nice day
For shopping/souvenirs, Hondori area is a must. Massive shopping area with multiple malls and souvenir shops. The PARCO mall there has a Shonen Jump Store and a Pokemon store for the kids or anime nerds in your life. This area is right next to the Peace Memorial Park and Hiroshima Castle. Took my wife shopping here after the museum.
Mazda museum is in Hiroshima as well. Never had a chance to go, but I've heard really great things.
Definitely had my fair number of days going to the castle/memorial Park, followed by Hondori, then night baseball game, just in time to catch the train back to Iwakuni.
Spoilered for length, but here's a list of restaurants in the area a friend and I put together (includes Sake breweries in Saijo and things to do on Miyajima Island)