You need a fast lens! As 103 indicated, it is hard to beat the FA 50/1.4. I shoot a lot of basketball, and my lens of choice is also the FA 50 f/1.4. Here are some of my recommendations:
1) Set shutter speed to 1/250. That is a good rule of thumb for stopping basketball action without blur.
2) Get to the gym a bit early so you can use the meter and take a few test shots. Lighting in a gym is pretty consistent, so you can go to manual mode, and keep the exposure the same in each shot. In our high-school gym, my settings are typically f/1.7, ISO 800
Here is a sample:
basketball game sample with FA50/1.4
For Radio City, your strategy will have to be a bit different since lighting changes during the show. Determine the best compromise shutter speed to stop motion. 1/125 may be a good first guess. Since lighting during a show constantly changes, manual will be cumbersome. Shoot in Tv mode at the shutter speed that you found to be best. You can also run auto ISO, or set it yourself.
Good luck and come back with samples!