I did the route with another van a couple years ago. It was great fun. Here's a write-up.
The entire route: Day 1 I met up with Jimmy and Suzie from Prescott, AZ, and their pup, Luna, in Las Cruces. The plan was to motel it there that night (Monday), and then slab it to Dell City, TX in the morning to start the offroad route. When I got the motel, they were already there...
www.overlandbound.com
Fly fishing? Down south, maybe the Rio Ruidoso or the Gila. There are a couple lakes too, Grindstone and Alta near Ruidoso, and Lake Roberts and Snow Lake in the Gila.
Up North, the Jemez river, the East fork of the Jemez, Rio Guadalupe, and the Rio San Antonio in the Valles Caldera. These are all small stream fishing. The Chama below Abiquiu lake is a little bigger and can be good depending on outflow from the dam. There's also Fenton lake and Abiquiu lake. Up by the Colorado border there's the Rio del los Pinos and just in Colorado is the Conejos. Both can be great!