Hey! Thanks I really appreciate this. Would you suggest not doing this for newbies?
My opinion? Yes i absolutely think you should do it, just change the plan a little. Jackson lake and the tetons are beautiful and not many people get the chance to sail beneath them. Given what you've got to work with I think overnight on the boat might be more work than its worth. So I would get a nice camp site at Lizard creek or something (get there early, like 8 am or sites fill up) and enjoy day sailing on the lake. I would go to leeks marina, and shove off from the dock with a gentle breeze so you can sail past the boats on mooring balls and be right in the middle of the lake.
Jordan pretty much hit the nail on the head. There are a couple things working against your goal, any lake campsites have been reserved since January, or they are "walk ins" which you have to be the first one at the back country office to get it, so if someone is coming off a weekend, you might be able to get it Monday or Tuesday. You can anchor on the lake (100 yards lol?! i didnt know that, i usually do about 10 ft from shore) and sleep anywhere and cruise the shore or islands during the day, but I wouldn't want to anchor and camp overnight in your dinghy (just a comfort thing).
I like colter bay marina, it has plenty of parking and the most facilities and is centrally located in the park, but unless you have a motor colter bay is probably out unless you feel comfortable sailing through the relatively windless chanel to get in and out (getting in with a breeze on the stern isn't hard, getting out on a calm morning, good luck). Theres a campsite in little mackinaw bay right at the mouth of colter bay, that might be fun, and not needing to haul your camp stuff all the way across the lake.
Leeks marina is fairly open so you can sail in and out from the ramp, its just where the biggest mooring field is on the lake, so you have to dodge the other boats.
The last marina option is signal mountain at the south end of the lake. This is by far the easiest to sail in and out of, nothing in the way, exposed ramp so you just push off the dock and go. Only bummer thing is its tucked away in the south end of the lake, so if you want to go sail right at the base of the tetons, its a long jaunt across the lake.
The wind on these lakes can be extremely varied and will swing around all 360 degrees and can go from 5 knots to 20 knot gusts real quick, so check the weather and get a feel for it first. Usually the wind is calm in the morning, and gets its best around 1-7 or so. Where is calms back down. So if you are out in the morning or early afternoon you might be doing more bobbing than sailing. Luckily in august its warm enough to swim and not freeze to death, or we bust out some fishing rods, or get our lunch going. Then when the winds pick up (10 to 15+) I can tow a stand up paddle boarder behind the boat under sail alone. Just have to take what the mountains and wind gives you.
Go to the gtnp site and find the back country camping site map and see where your options are, and check out google maps for the marinas I described. Let us know when you'll be in the area, and ask any other questions you come up with!