a 노래방 is pretty much the same in America as it is in Korea. Just go in, and have a good time with your friends, jumping, screaming, etc. It'll be fun depending on the songs you pick and the friends you go with
For the most part, 노래방 will have modern songs and music. If you live where there's a lot of 노래방's, then there chances are they'll have up to date songs. If there aren't many of them around, they can still have modern songs, but they might not as well
Hope you have fun, and rock out while you're there! I love 노래방!!