Welcome to backcountrypost,
Boerboel!
There is so much to do on Hole-in-the-Rock although the plan of day hiking out of your base camp generally doesn't work down there with how spread out everything is. Here is my list of recommendations on places to hike:
Fortymile + Willow Gulch Loop
About 10-12 miles depending on how you connect the loop. One of the best hikes down there, IMO, but could be a bit cold through the narrows of Fortymile this time of year. There is one chest deep pool and a fair amount of knee deep stuff. You could always play it safe and just go down Willow Gulch and explore up Fortymile as far as you feel like. Broken Bow Arch and the great alcove across from it are very cool to see.
http://backcountrypost.com/forum/index.php?threads/fortymile-willow-gulch-loop.133/
Hole in the Rock
If you have the 4WD, it's fun to drive it all the way to the end and climb down the crack where they took all the wagons back in the day.
Coyote Gulch
One of the best around and for good reason. You might still have some leaves hanging on the trees if your lucky. You can day hike in from the top or bottom or you can make a loop going in at the Water Tank TH either via Hurricane or Hamblin and then out at Crack in the Wall. The days are a bit short to pull off the loop as a day hike but it could easily be done as an overnighter if you keep moving.
http://backcountrypost.com/forum/index.php?threads/coyote-gulch-loop.65/
Egypt Bench
There are a bunch of technical slots on the Egypt Bench if you're into that, or you can day hike from the Egypt TH down to Golden Cathedral in Neon Canyon. If you take the B-Line, it's about 5 miles each way and it's a beautiful hike. If you go through Fence Canyon it's probably a mile longer. There are some fun little slots to play in and around if you take the Fence Canyon route. You could always make it a loop and go in one way and out the other. Let me know if you need specifics on the B-Line route.
http://backcountrypost.com/forum/index.php?threads/into-the-escalante.1482/
Bighorn Canyon
An incredibly beautiful non-techincal, dry canyon that connects Harris Wash to the Old Scheffield Road (aka Spencer Flats Road). When I did it we approached from the bottom and day hiked up a few miles but there is a better route if you start from the top, get into Harris Wash and then walk back over the bench. You can even add Zebra/Tunnel onto it if you hike fast, although the short days might make that tough.
http://backcountrypost.com/forum/in...in-the-rock-and-bighorn-canyon-escalante.454/
Harris Wash
Meh.
http://backcountrypost.com/blog/escalante-area/harris-wash-may-2008/
Red Breaks
I haven't been to Red Breaks but the slot looks like a lot of fun. Do a search for it here on BCP, there have been a couple of good threads and trip reports on it lately. The big dome above it is cool too, it goes by many names like Cosmic Ashtray, Escalvolcano or my favorite, Islomania Dome.
Batty Pass Caves
Haven't been there but they look cool. They're down on the lower half of the road on a side road up towards Fifty Mile Mountain. Someone on here like
Seldom Seen Anderson could probably give you coords.
Spooky, Peekaboo and Brimstone
Great slots in Dry Fork Coyote Gulch. I haven't done them but they're very popular. Caveats: one of them (I think Spooky) is too skinny for those with larger frames and dogs are not allowed.
As far as car camping, there are not a lot of great spots along HITR. I can give you some specific recommendations based on where you think you might end up.