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Ok time for some real advice. I've been drinking so you can trust me.
You're going a little overboard. I know she's prissy, but you can rough it just a litttttttle bit more than a "summer camp".
Lots of places have cabin rentals. As a tip try going to Google and searching for "cabin rentals".
You don't need a bunch of activities scheduled at some outdoor summer camp. Just get a good pair of shoes, more on this later.
Seriously. Just rent a cabin. Cook meals for you? Nah, bring food to cook yourself. Most cabins will have some kind of grill. Bring some good food to cook up, you'll add to the experience. Cabins are just like homes basically. They are warm, dry, and comfortable. They will range from being 1 room with a bed, to a 3 bedroom house. Fine one with a bathroom at least for your girl.
Now for activities. Find a state or national park. Go there. That's where your cabin can be (at least close to the park). Just get some hiking shoes/boots and hike. Pick a park that has some beautiful scenery. You'll be amazed how rewarding she will find hiking a short distance to a beautiful sight. Bring a camera, carry a backpack with water and a knife if it makes you feel more outdoorsy.
Start small. Go for 2 nights. Get there and set up one day. Hike the next day. Sleep, then leave the following day. She will get a taste without being put off by sleeping in a tent for a week without showering.
Bring some wine, she'll like that. Make her a good meal on the grill, and see a few things at a good national/state park. Kiss her under a waterfall if you have to.
Hopefully she will like it. Part of the fun of being outdoors, for me anywyas, is being a bit uncomfortable. Not showering, being dirty, sleeping in a hammock and waking up with the morning fog. She won't like that right away. Start small, and work up. She may really enjoy it.