I brewed my last batch on a friend's back porch. @atom has the right idea, you need to make a thorough list of the equipment you want to have, and then just have fun!
Some thoughts:
1. Try No-Chill - It doesn't get much easier post-boil than this.
2. Try BIAB - Much easier to just need the one big pot, plus a big pot is always handy camping
3. Brew Primative - Use that campfire for heat, scoop your strike water straight out of the creek, it saves on packing and gives you a more memorable experience! Barkeeper's Friend will fix all the soot on the outside when you get home, and boiling will kill anything in your water.
4. Brew something Interesting - If you follow #3, you'll get faint smokey strike water, how about a Classic Rauchbier inspired IPA, or a Smoked Porter? Make it your "campfire brew" and include chocolate and vanilla to get a Smores effect?
5. RDWHAH - Worst case scenario you're dumping the wort when you get home. Have fun.
6. Leave the Yeast at Home - If at all possible, sanitize and seal everything up tight and skip pitching yeast until you are back home.
I almost forgot the important part! Invite your campsite neighbors to come over! You'll convert at least one of them to home brewing if you brought a few bottles of one of your previous brews, and you showed them how simple and fun brewing can be.