The Grandstand near a bus stop is what I always request and it's about a 5 minute walk to the lobby. I've also stayed at the Paddock, and that's about a 10 minute walk to the lobby. If you don't want to walk, you can also get on any theme park bus. The last stop before they leave the resort is the lobby. To return to your room, get on the DTD bus but remember it usually doesn't start running until around 8 or 9 am.
Not sure about the gym...I never use it because I do so much walking when I go to WDW that I figure I've gotten enough exercise. If you wanted to see a resort map, I think there's one on wdwinfo somewhere.