Like other large Japanese cities, Hiroshima is serviced by the shinkansen and local trains. It is serviced by a small national airport with occasional flights to China.
Day 1: Peace Memorial Park
Peace Memorial Park occupies an island over which the first nuclear bomb was set off during WWII. The insland contains numerous memorials, extending out to the "Atomic Dome" building off of the island, as well as the Peace Memorial Museum. The museum cintains some graphic content, but tells the story of the consequences of the atomic bomb, start from the initial explosion, through radioactive fallout, and on to subsequent effects of radiation exposure. Although the museum is well put together and very informative, some may find the content disturbing, and the portions discussing backdrop of WWII have a certain nationalistic viewpoint.
Day 2: Miyajima
Itsukushima is an island just off the coast of mainland Japan in the Seto Sea, and it takes about 30 min train plus a 10 minute ferry to get there. The island is popularly known as Miyajima, meaning "shrine island," due to the presence of the Itsukushima shrine. The shrine is built a beach with a very low declination, which causes it to dry out or be filled with flooded canals depending on the tide. The infamous O-Torii, a red gate built offshore of the shrine, is accessible by foot at low tide. Another temple complex nearby features a massive main hall and a five-storied pagoda.
In addition to the shrines, the other main draw in Itsukushima is Mount Misen - immediately obvious as son as you board the ferry. The hike up the mountain takes about 3.5 hours, but this can skipped if you wish by taking the cable car. As the highest point for some distance, there are sweeping 360-degree views of the mainland and various islands in the Seto Sea. While on the sialnd, you may run into more friendly deer throughout, but the hike gives you your best opportunity to spot local monkeys.
Taking the shinkansen back to Tokyo to access Narita International Airport, or to Osaka for Kansai International Airport are your best bets, as flights from the small Hiroshima airport aren't necessarily much faster. Note that travelling from Japan to North America crosses the international date line, so you will arrive on the same date you left.