northern NM has a lot of different areas, best bet is to pick an area and then call the local fly shops and see what hatches will be going on while you're here. The San Juan is still fast and muddy in the spring and it can be a frustrating river even in the best conditions, picky trout.
Jemez has some great fishing for Native Browns, just have to sneak up on them and present them with something they like... just look around and the hatch will tell you what to fish. Timing for the Jemez is great spring to fall, with late spring early summer being the best maybe.
Pecos is great as well, but park and hike up river to get away from the crowds, again spring to fall and hit the local fly shops for advice in whats hitting while you'll be there.