Hey there!
From the game manual (found in the dropdown list):
"1. Gym - training is hard, but a well equipped gym will motivate players to spend extra time training, giving a wider range of skills a slight boost. The effect is very similar to the already existing cross training, in essence, the gym is giving your team more cross training "slots". Higher gym levels provide more personal trainers and additional equipment, giving the team even more cross training "slots".
2. Training Court - spending valuable training time on free throws is always a hard bargain, most teams opting to do in the offseason, when normal training minutes are harder to achieve anyway. The training court will enable players to work on their free throws during the season, additional to normal training. The effect is not nearly as large as dedicating a full week of training to free throws, but at least those weeks will not be necessary as often as they are now."
*I do not have either, so I can't speak on their value.*
Additionally, training updates occur every Friday. As you probably know, rate of skills improvement is correlated with level of trainer. I have a superior level trainer and see about 3 skills pops/wk.
Very happy to see a new member replacing a bot team.
Best of luck!