Santa Fe- Dalton Canyon by Pecos has crinoid stems, horn coral, and brachiopods from the late Paleozoic. Up by the ski basin they find similar items.
Albuquerque - There are many areas where late Paleozoic marine fossils can be found. The top of Sandia Crest, which towers over Albuquerque, has limestone formations with abundant crinoids and other marine fossils. Also, there is a particular spot in the Jemez Springs area near Battleship rock. Park beside the road near the monument (there is a charge for parking in the parking lot) and hike back south along the road. Along the west side of the road are occasional outcroppings of limestone with yet more crinoids and other fossils.
On route 475 - the road from Santa Fe up to the S.F. ski basin. About a quarter of a mile past Ten Thousand Waves is a small pull- off area on the right with several 3-foot diameter boulders. Park there and walk along the roadcut just a little farther along. This is an outcropping of Pennsylvanian limestone and has lots of brachiopods and nicely preserved crinoid columnals. The fossils are in hard rock, however, so look for the layers which have weathered the most so you can get them out.
The Jemez mountains--start in Los Alamos, then out route 4 through the Valle Grande. When route 4 meets route 44, turn left. Approx 2-3 miles further along you will see a turnoff for Battleship Rock to the left. Just across the main road from the turnoff is a nicely layered outcropping but it doesn't have anything. If you climb the hillside across the road, above the lower outcrop, however, you will find lots of outcroppings of Pennsylvanian limestone which are packed with crinoid sections and brachiopods. The best hunting is in the areas where small stones and fossils which have weathered out of the rock get swept by the rain.
Outside Lamy, a tiny town SW of Santa Fe -- behind the church graveyard (ask for instructions how to get there) is a hillside with outcroppings of grey-green sandstone. Off to the right and back up in the hills is an arroyo. If you walk up the arroyo and pay close attention to the stones, you will eventually reach an area where there are tons of ammonites of all sizes (up to a foot across) and many different species. Unfortunately they are poorly preserved (the original shell material crumbles away or is not present) in crumbly sandstone so it is nearly impossible to get good specimens.