Jennifer,
I am sorry, but I have not been able to get a really great answer for you on this question. There is one solution, but it is a pretty pricey one.
You can actually get game tickets that include time on the actual field. It is known as the
On-Field Spectator Experience. What it entails is getting to watch warm-ups from on the field, right behind home plate. This is an extra charge over the price of your standard ticket that you need to watch the game. But it does sound like a pretty exciting opportunity, if it is within your budget.
As for places to catch players outside the ballpark, I have not been able to get any specific ideas on where you would be able to do that. What I recommend is that when you get there, ask one of the Disney Cast Members that works at the Wide World of Sports venue. They would know, and should be able to give you some ideas.
Sorry I can't give you more options!
Have a magical vacation!