I would suggest going to the Carlsbad Caverns. I went there a couple of years ago and had a great time. We did a tour in the dark with hardhats and lights which was really fun but you should register for the tour as soon as you can because they do book up. I have heard the white sands national monument is a great place to visit but I didn't get a chance to go. The gondola up the Sandia Mountain was OK. Bit expensive and there's not much to do at the top besides eat in the restaurant. If you like Thai food, I would recommend the Thai House on 106 Buena Vista Dr Se Albuquerque NM. It's near the University. It doesn't look like much from the outside but the food is excellent!
In Taos, the Millicent Rodgers museum was fantastic - an ex-East Coast VERY wealthy woman who truly understood what Taos and NM are all about
Opera in Santa Fe is great. In Santa Fe, the best time to eat at the best restaurants is for lunch - great prices, same menu
Driving from Santa Fe to Taos - take the back roads
Bandalier National Monument is fantastic - but you HAVE to take the drive to see the caldera - it's on the way from Bandalier to Los Alamos
Spacing on some other things - but there was a slot canyon south of Santa Fe with a manageable trail - can't recall the name - but a gem
Carlbad Caverns is a great trip, although the best part you would be missing, since you are going in April. In the evening, from mid-May to mid-October, the bats fly out of the cave and it's an amazing sight - 400,000 bats fly out in about 15 minutes. There is a small amphitheatre built into the rocks, so it's a real show.
Other small towns in that area are also exceptional, such as Ruidoso - reminded us of a New England mountain town.