Such a cool area, and a really awesome place to hike around and explore. You can walk among the hoodoos, which are like nothing I've ever seen, and get some out-of-this-world photos. Like Anna said the park is pretty out of the way, but Highway 24 is an awesome drive and park is absolutely worth a visit.
Very cool sculptures! Just by the side of the highway as you drive out of Hanksville, in front of what appears to be an abandoned motel. Snap a few photos and marvel at the handiwork that crafted these awesome sculptures.
Found the World's Largest Watermelon outside the Green River police station. Since the wooden statue is on wheels, it moves around from time to time, so you have to be willing to explore Green River a little bit for this photo-op. While in Green River be sure and grab a watermelon of your own--the desert climate is ideal for growing watermelons, and the ones in Green River are some of the most delicious watermelons I've ever had.
If you're traveling along the scenic Highway 12 in Utah, definitely make a point to stop at Blondie's in Hanksville. Located right next door to the awesome Hollow Mountain Gas Station, Blondie's serves up ridiculously cheap and ridiculously delicious burgers made from local, grass-fed beef. Be sure and get a milk shake too--they're the best you can find in all of Utah.
If you're traveling through the southern Utah area, DEFINITELY stay here in Boulder at the Boulder Mountain Guest Ranch. It's a bit off the beaten path, about three miles from Highway 12 (aka the Devil's Backbone), but absolutely worth it. The area is beautiful, and the guest ranch provides an awesome (and cost efficient) stay. The main lodge offers stunning views of the area as well as the delicious Sweetwater Grill (featuring organic food grown in the Guest Ranch's own garden), and the accommodations are wonderful as well. If you get the chance, try and sleep in one of the Guest Ranch's tipis--there's nothing cooler than sleeping under the stars in a queen bed housed within a beautifully-crafted canvas tipi.
Awesome place to check out if you ever find yourself strolling through Georgetown's main street. Bierstadt has a nice collection of books as well as a great balcony area with more books and a sunlight. They also serve coffee and a selection of pastries, and are adjacent to a super cool art gallery.
Kneisel & Anderson is so cool! The space has been operating as a grocery store continuously since 1881, and is full of imported and special-order food items. Check out the tea canisters along the wall behind the counter, which have been there since the store first opened.
Great place to stop and check out on your way either up or back down from Mt. Evans. Their food is delicious, especially the home made pies that are made every morning. From the bar area you can also get a beautiful view of Echo Lake and the mountains surrounding it!
Full Steam Ahead is a great little coffeehouse right outside of Red Rocks! I stopped by here after filling up at the gas station next door--their coffee is awesome, and it's got a nice space to sit and relax in.
This place is filled with t-shirts and a lot of other tourist paraphernalia. It's a central place to start a hike through the park though, and when a band is playing Red Rocks you can usually see their roadies loading and unloading gear near here.