I'm partial to the state parks in New Mexico. I've been to most of them, but prefer the ones in northern NM. A few of the don't miss:
Sugarite Canyon State Park: Site of an old coal mining colony near Raton. Nice guided hikes are available and fishing is good at two lakes in the park. Also close to Johnson Mesa and within driving distance of Trinidad.
Clayton Lake State Park: An oasis in the desert. Dinosaur tracks were discovered when it was built and you can take a short hike to see them. Nice fishing and hiking. Near Clayton, and a good overnight or two day stay on your way in or out of NM.
El Vado and Heron Lake State Parks: Two lakes that are very close to one another. Heron Lake is the northern Lake and completely within the park protected from development. It is known for being a no wake lake where sailboats are welcomed. Lots of nice camping spaces. El Vado is the southern lake and has some development around it. It allows motor boats, but the level has been so down in recent years that most people only jet ski. Good fishing at both lakes (notice a trend here?), but the real gem is the hiking. There is a nice trail along the Chama River that goes between both parks that is absolutely beautiful. Worth going for that trail alone. Near Los Ojos, a weaving community, and a short drive from Chama.
Coyote Creek State Park: A nice little park known for it's great trout fishing. Great campsites and a very beautiful mountain meadow feel. Some hiking trails are available. They have just installed a nice playground, so if you have small kids you'll enjoy it. North of Mora and near Morphy State Park.
Morphy State Park: A small park but containing an absolutely beautiful true mountain lake. Here you will be nestled in the pines. Fishing is nice and hiking is OK. You'll enjoy the isolation and ability to get away from civilization. Because of the size of the park, road and campsites, RV campers are limited to 18 feet. And, trust me, they mean it. You don't want to have to try to back a 35 foot trailer back down the mountain road.
Fenton Lake State Park: My absolutely favorite of the state parks in NM. We usually stay in the National Forest (the San Antonio campground on the San Antonio creek is the best IMHO). Fenton Lake is another place that is a beautiful mountain lake in a small(ish) park. The lake looks like it is right out of a post card, with big pine trees surrounding it, water lillys in the shallows and green grassy banks to fish from. Go in the winter to ice fish if you are adventurous. The area surrounding is national forest, and it is full of hot springs, so there are all levels of hiking trails to choose from. This park is north of Jemez Springs, a quirky community with no gas station, but with a spa where you (or your significant other) can take mineral baths and get a massage and then go for a cold beer and fried jalapenos at Los Ojos restaurant. For bonus points take your better half to Jemez Fine Arts (in a former gas station) or Jemez Pottery. If you go in the winter (for ice fishing) be sure to reserve a sleigh ride at the Valles Caldera. This is my secret don't miss it tip. If you are a fan of wildlife spotting, the Valles Caldera is the place to do it. On our sleigh ride we saw a herd of elk in the snow and it was breathtaking.
We live in Lubbock, and all of these places are a relatively short trip for us. We have an RV and have camped at all of the above, except Morphy Lake because we were too big. One of us likes fishing, the other hiking, and these parks give us the ability to do both. We tend not to spend lots of time in towns.
Northern New Mexico and Southern Colorado is where we spend most of our vacations and we love it.