There are lots of Anasazi ruins in and around NM, but my favorite isn't the famous Mesa Verde, it is Bandelier National Monument.
There are many reasons it is my favorite, but the number one reason is that it is in the Jemez Mountains which is probably my favorite area in all of NM. I will no doubt talk more about Jemez in the future.
Whenever someone is visiting New Mexico I send them to Bandelier (sometimes I go with them) and I have yet to have anyone be disappointed. Sure they could make the long drive to Mesa Verde, but they could be at Bandelier in about 2 hours.
What do you get once you are there? Beautiful surrounding mountains, lots of wildlife such as mule deer, a nice little hike, a really cool kiva, cliff ruins, valley ruins and painted cave.