It's only a few years old... on the other side of CityWalk from Universal. You can get tickets that get you into both parks. Islands of Adventure is much bigger, has more to do, and most of the best rides I went on were there.
For the best shows, hands down, Disney has them. Fantasmic at at MGM is incredible and Disney's Electrical Parade at the Magic Kingdom is pretty cool too. MGM also has Lights Motors Action and Beauty and the Beast which are cool. The rides at MGM are pretty dated, though, so if you are going there make sure to get good seats for those two shows.