I'm so glad you love the idea, Jill! And thank you for following up with me; getting questions sent directly to me makes my day! As for the golf course, I've not visited either so I can't really offer a tried and true perspective on which is better. I can tell you, though, that
Fantasia Gardens is within reasonable walking distance of the BoardWalk area (Epcot resorts). It would sure be easiest to visit that one.
To park, just pull up to entrance to the resort (it doesn't matter which). There will be a Cast Member working in the "gatehouse". Just tell him or her that you would like to visit the resort and that you'll be eating at Beaches & Cream. He or she might ask to see your photo ID, so be prepared for that. As long as they aren't operating at full capacity, you should be permitted to park your car for a few hours and explore the area. When you're ready to play golf, you can just park in the lot there (free of charge) for the duration of your golf game. Have a fabulous first day (okay, okay, have a fabulous every day thereafter, too!).