I agree with Troo about something local. Food items are also a good idea as you can enjoy them with your friends. When I organized a tour of women from Michigan they brought dried cherries and shared them with their home-stay family. Everyone seemed to enjoy it.
I do not know much about concerts but there are quite a few "Live Houses" in most major cities. Just do a Google search like "live house Osaka" or wherever you are visiting. Also the
Japan Times lists concerts.
Good luck with the heat and carry some small towels to wipe off sweat. You can get these at a 100 yen shop. Clean ones also make fun, cheap, easy to carry omiyage (souvenirs).