That time of the year would be fun around Santa Fe. Places to check out are the Jemez, west of Los Alamos and the Pecos, east of Santa Fe. If you want cutthroats, either place will be fine. Just remember the higher you go, the better it is. On the Pecos, you can catch Rainbows and Browns down lower. Same on the Jemez. The Jemez is fed from the Guadalupe and the E. Fork Jemez and the Rio San Antonio. All are fun and good. Think 2-3 wt on the feeder creeks and a 4wt on the Jemez. The Pecos 4-5 wt rods work well. Check in with High Desert Angler in Santa Fe. They know the area the best. I used to live in Los Alamos for 4 years and never ran out of places to explore and never got to all of them either. Have fun! New Mexico is a well kept secret and once you discover it, you almost want to keep it to yourself. The San Juan is well known, but not the only place to throw a line. Oh, and the Rio Grande is also within an hour or so and if you want to challenge yourself, go there. I can’t recommend anywhere else to send a hot shot to get humbled! It is rewarding though. Hope this helps.
Juan