If you haven't been to Crown King, it's a great place to visit. Try out the old saloon for a post-hike beer. There's a lot of interesting history you can read up on (available from numerous sources). There's a small B&B and some cabins for rent so you can stay there in the summertime as a base for recreation. Its not as bad as the Beeline/4-Peaks area in winter, but quads are a common scene up here.
Horsethief Basin probably doesn't deserve the huge sign on I-17. At least not because it's a great "Recreation Area." I've been there several times, but except for a few short hikes from a campsite once, I've never actually hiked there. Horsethief Lake is a small body of water that is dammed and stocked with fish (at least in summer). By small, I mean a Safeway store covers more area. There's usually a few people there on the weekends fishing. The lake is in an area with some private cabins/private land, and some closed roads accessing them.
Crown King and the areas above it such as Towers Mtn are typical of higher-elevation Arizona, with ponderosa pine and gamble oak providing ample shade. However, Horsethief Basin is a bit lower in elevation, and while there are sporadic strands of Ponderosa, much of the landscape is dominated by lower-growing pinon, juniper, and chaparral. I would compare it to what you find in and around Payson.
I once tried to drive to the Horsethief Lookout tower, but encountered a closed road before I got there. It was a hot summer day, and I didn't have the effort to look for it on foot. Though not technically in Horsethief Basin, I did enjoy a short hike to Poland Creek (Algonquin Trail #225) once.
http://hikearizona.com/decoder.php?ZTN=9 I don't ever recall seeing the sign for any other trails, but the HAZ writeup and photos indicate that this trail connects to Horsethief Basin. I recommend the Algonquin Trail in Spring/Fall as it can get warm during the summer.
You can get to Crown King from I-17 in a sedan, but it will take you an hour on the dirt road. Past CK, and down to the basin requires high-clearance, and 4WD in wet weather. You can also get to CK from Prescott via the Senator Highway, which also requires high-clearance and sometimes 4WD. (Don't let the name "highway" fool you. It's a rough dirt-road.)