Although most people only know Hiroshima for the tragic bombing that took place back in August 1945, the modern version of Hiroshima is quite cosmopolitan and charming. The city has a great nightlife, good food, and a population of approximately 1.2 million people.
Most people travel to Hiroshima via airplanes or trains. It is served by its own airport (Hiroshima Airport), and it is also a part of the Shinkansen line (the famous bullet train). There are also long-distance bus services that you can use. Moving around the city itself from your Hiroshima hostel is best done by either using the public transport system or taking the option most locals use: biking. Like most cities in Japan, Hiroshima is absolutely great for biking, and this is one of the best ways to get around the city.
Hostels in Hiroshima are of good quality. The prices for dorm beds vary, but you should be able to find a bed for about 20 - 25 US dollars a night. Remember to ask hostels for bikes / general information, as you can get discounts if you book things / rent bikes through them.
The incredible history of the city is unavoidable. While staying in a Hiroshima hostel, most people visit the Peace Memorial Park, which contains most of the A-Bomb related things to see. You can easily spend a full day in the park because there are plenty of museums and a lot of things to learn. My advice would be not to only go see the most obvious things, but to look also for other cultural experiences while in the city, as Hiroshima holds much more than what first meets the eye.