I think it is a bit too late. The Itsukushima Shrine in Miyajima will be closed at around 17:00. I think you can take the earliest morning train/tram to Miyajima-guchi and visit the shrine in the morning, as it is open from 06:30. You should have enough time for the Peace Museum and the Park until 2PM or so.
You might stay at a ryokan in Miyajima though, if you like. The short ferry is running until 22:42. However, there is practically nothing open around that time.
If you stay in Hiroshima City (which I recommend over staying in Miyajima), I recommend visiting the Okonomiyaki Village.
Although Hiroshima is a fairly large city, there aren't so many things that you can do after 20:00 or 21:00, other than to have dinner and have some drinks at a bar. There are usual entertainment opportunities that you'd find in any Japanese city, like Izakaya taverns, Karaoke boxes, batting centers, bowling (please google map search). Donki discount store open until 05:00 in the morning: www.donki.com/search/shop_detail.php…
There should be a spa house too somewhere, if you want to relax in a hot large bath and perhaps take a massage.
I imagine that 20:00 would be a bit too late for a baseball game.
Edited: 9:01 am, January 28, 2013