All the Arkansas sections are worthy... Brown's Canyon, Fractions and some stuff on the way down to Canon city are all Class III, Royal Gorge is III-IV depending on the level.
In New Mexico, the Chama is too low (day section that ends at big eddy) on the Rio Grande the Lower Box is III-IV wilderness run that is much more challenging in a raft.... (NR) at low flows unless you have a 10-11' boat and know the lines. it is very technical and a lot of work (in a raft)
its a blast in a kayak, but a long day and committed ( 17 mile run in a Box Canyon with no egress) search the other recent posts for beta on it.
The easy roadside class III option is Pilar race course south of Taos. thats our most commonly run easy stretch, with camping and everything nearby, and non-stressful rapids. (road scout Big Rocks rapid below the low wooden bridge- its the only hazard on the run, a tight channel called the slot on the right, and the Toilet bowl on the left. both are fairly easy but there are bad undercuts on both sides of the mid-river boulder so there is consequential moves to be made) RC is easy fun run all the way down to 2-300cfs (same thing, pretty technical in a raft)
Hope that helps