If you land the 1500 loop you will have a great space for throwing the frisbee. When you exit 1500 you will be facing a canal, and just across the canal is a large open space between you and the pool. There is an area set up for volleyball but plenty of space left over for frisbee throwing. I have provided you a map. The area circled in red is directly across from the entrance of the 1500 loop. There is an area called Creekside Meadow close to the 2000 loop (circled in blue) that may be open. This is an area sometimes used for primitive camping and can very well be filled with tents or completely empty. Finally, if you are willing to ride the golfcart or your bikes, there is another area (circled in purple) along the entrance road that has lots of open space on both sides of the road to play.
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There are other areas scattered around the Fort, such as around Pioneer Hall, down on the beach, etc. that are available as well. These are just the locations that I can think of close to your sites.