They just started releasing water in the Cimarron again. It fishes better with at least 15 cfs. I recall some spectacular caddis hatches during the first week of July, but stoneflies and mayflies are possible. Recommend checking the flow rate before going:
https://waterdata.usgs.gov/nm/nwis/uv/?site_no=07206000. Fishing is better in the “Green Chile” water marked with signs. You have to stop at the upper camping ground to pay for a $5 parking pass.
The Hondo, Rio Grande, and Pinos are currently running too fast, but they may be good by the time you get there. I heard they poisoned Costilla Creek in Valle Vidal to stock native cutts again.
The Pinos is my fave in the Green Chile section, but it is a couple hours drive. So is the Conejos. I recall a nice slate wing drake hatch is possible that time of year. Green rockworms are common in the Pinos. Check local fly shops as much depends on the flows.