Okay, to post a bit more. I don't know much about camping but I can tell you about my experiences in some of these parks and hikes that will be good to do.
Badlands NP
Great to drive through - the road system is really nice and you can access a lot of vistas and cool spots right off the road. I'd recommend doing a short hike, not more than an hour or so, so you can get on top of some stuff...but you'll see a lot from the road.
Yellowstone
What you put in is what you get out, here. So much of the park is really "accessible," which confused me a bit. On one hand, it's great that its so available for all to see but on the other, its kind of lame to see 300 lb park rangers waddling amongst 300 lb park visitors seeing spectacular natural stuff that you usually have to work really hard to get to. It was just interesting, is all.
Thus, for the main stuff at Yellowstone, it's less about hiking and more about planning your day. Old Faithful is cool, but everyone and their mom stops there. If you're willing to walk, there's a short hike to an overlook that would give you an awesome view. When you're standing on the platform by the rail with the cafeteria behind you (lol), look right up the hill, and you'll see the overlook. I haven't been up there but it shouldn't be hard to find.
The Rainbow pool (or whatever it's called) is super cool. It's neat to walk the boardwalks in it, but I recommend going a little bit farther down the road (towards Old Faithful) and stopping at the next turn in. From there, you can walk down a dirt path and then up a hill side (it doesn't really look like you're supposed to be there, and maybe you aren't) but you get an awesome view down on the pool and you can really see the different colors.
There's a ton of other stuff at Yellowstone, but for the most part I didn't see a lot of that. I went with people who hadn't been there before and I found it hard to make it off the beaten path. I think Yellowstone is an unbelievable environment and really worth seeing, but I'm not sure I got much out of it (and I've spent multiple weekends there). I'll need to go back.
Tetons
So sick. You'll love the Tetons. How fit is your group? Depending on how in shape you all are and what you're up for, I can recommend you a number of things. I spent a good bit of time in the Tetons two summers ago and can give you some directions.
Disappointment Peak is a great hike if you only have time for one. It gives you breathtaking views of the main Teton peaks (except Moran) and an unrivaled look down into the valley. There's a lake to swim in on the way up, and a couple scrambles to entertain you amid the walking. Too fun.
http://www.summitpost.org/disappointment-peak/153638
If you're trying to go harder/farther but don't have climbing gear, the Middle Teton was a great hike. I did most of it in the dark with people who knew where they were going. I don't think I'd do this one without a guide or experienced friend, but I'd be happy to hook you up with a name if you're interested.
http://www.summitpost.org/middle-teton/150981
In addition to these two (which were my two favorites), there are a number of smaller hikes around the main areas of the NP. I'm sure a lot of these will be great, if slightly more crowded. If you're feeling adventurous, you can access the Tetons from the backside, which means you don't have to pay. If you come in from the other side (Driggs), you'll be on the same side of the range as Grand Targhee. Table Mountain is an awesome hike that brings you right up to the backside of the Grand. Alaska Basin is unbelievably expansive and really beautiful in the summer. Both are places you wouldn't get to from the frontside without backpacking.
http://www.summitpost.org/table-mountain/152764
http://www.summitpost.org/alaska-basin/700323
MAKE SURE YOU HAVE BEARSPRAY. Wear bells, keep track of your food, and be smart.
Zion/Bryce
I went to these two when I was much younger (with parents) and most certainly need to go back. There are tons of Utah NSers who could tell you more about these.
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I haven't been to Arches/Heber but I'm sure they're great. I still think you need to sit down and really plan what's realistic for you to do in your 2 weeks. Considering that you have to factor in all that travel time, I think the number of places you want to check off (and I really mean 'check off') is absolutely unrealistic. IMO you should divide your trip in half (1: Badlands, Devil's Tower, Rushmore (not included in the NP pass), Yellowstone, Tetons; 2: Heber, SLC, Zion, Arches, Bryce) and do the other half another time. I think you should maximize your time in each spot so that you're not missing out on experiences in any of them and so you're not stressing about fitting it all in. This is supposed to be a reward, a nice fun trip with your friends, not a frantic race to see and do too much.
