Do whatever hikes you can in the Chisos (Window, Emory, etc.). Santa Elena, Hot Springs and the Balanced Rock at Grapevine Hills are also good places to see outside of the Chisos. The weather will be either mild hot or cold, so prepare for all 3. You are going during the busy season, so if you are planning to camp in the Chisos I hope your arrangements have been made as it is often full-up in March.
Read and heed this link
Oh yeah, drive whatever roads you can with your vehicle, be they paved or offroad with a 4x4; it's a great way to see the park. Just drive prepared.