If you can get a wilderness permit (pretty cheap) for any of their backcountry trails, you get to stay at the backpacker's camp the night before your permit is active (and on the last night I think). There is one inside Yosemite valley with first-come-first-serve spots and there are plenty of low-demand trails that you can probably line up with your trip. If you want to get the most out of it....actually use your permit and hike for a few days as intended....or not.