Type?
The majority of the rocks within New Mexico are either sedimentary (usually limestone or sandstone) or as jkl said lava rocks. Individual areas that are going to have some kind of interest rocks are either state or federal parks. They are sometimes bordered by BLM land or private land where you can collect but not always. City of Rocks is not a bad place with an abundance of fused volcanic ash. You might be able to find some small specimens in legal areas that have been smoothed by wind and dust.
If you are specifically looking for smoother, more polished rocks, I would suggest trying next to the Rio Grande from about Bernalillo north. Additionally, if you can find a lava flow (usually in the back woods) where the lava flow met the river, you might be able to find acceptable obsidian or jet (State Road 152). This is generally in the center of the state though. As far as north goes, you might be able to find something at the foothills near Sandia Park and the Sandia Mountains. Otherwise, you could also check north near Los Alamos in the Valles Caldrea area. You are still going to primarily get igneous type rocks but you might be able to find metamorphic at the edges where it meets the limestone/sandstone
Also, as a reminder, please do not take rocks off of a Park area. The same precautions mentioned above also go. Additinally, please make sure and take water with you, know the region, tell someone you are going, and if you go during the months of April/May-August/Septemeber, please watch out for our scaled neighbors.