I've been there, and would recommend it as well. I actually went at Christmas break, but had great weather there.

It's been several years, but I got a $3 package of info from the park itself that was very helpful.

The scout group I was with did some dayhiking in some of the canyons and also an overnight backpack up in the mountains and around the canyon rim. I'd have to hunt my map up to tell you the exact route.

Guadalupe Mountains National Park has some similar features, and is worth visiting as well.

One thing to keep in mind, is no campfires. I went up in the Guadalupe Mountains twice, around Halloween and around Thanksgiving, and got snowed on a bit, both times. But what I remember is that about 6:30 or so, it got dark, it was windy, no campfires, and there was nothing you could do but climb in the sleeping bag and wait 12 hours. There was also no water up high, and I ran out and had to hike about 5 miles down and 5 miles back up just to refill my water. I remember taking some star pictures with time exposures in Big Bend that came out pretty neat.