Check out the
What To Do web page on the official BBNP site for the usual recommendations. Unfortunately you may not get the best impression of Big Bend during spring break due to the crowds. Of course, keep in mind that I thought the South Rim trail was crowded because we saw about twenty other people on it, so I guess it depends on what you're used to.
The Lost Mine Trail is a definite must-hike. Most people hike down to the Window as well. If you do, I recommend taking the Oak Springs Cutoff trail up to the rim where it overlooks the desert. You can do that either before or after going all the way down to the Window pouroff. Of course, you'll need to drive down the Ross Maxwell road, stopping at all the viewpoints, until you get to Santa Elena Canyon. And, in the opposite direction, you'll need to go check out Boquillas Canyon and maybe the Hot Springs for a good soak. Grapevine Hills is another good short day hike, although you'll have to drive on a bumpy gravel road to get to it. If the weather is not too hot, you could try hiking the Chimneys Trail from the Ross Maxwell road. For something more adventurous, try hiking out to Mule Ears Spring and back from the overlook. If you find hiking in the mountains to your liking, hike up to Emory Peak and scramble to the top. It's a workout, so plan on taking your time and enjoying the views.