Westwater is a classic desert canyon about an hour to the west of grand junction. In march its running at good flows for play (low) and has some nice waves for surfing. Its 17 miles, is well away from the road on the run, has lots of flatwater, some fun class III in the middle of the run, and along flatwater paddle out. Shuttle is about 1.5 hrs.
The shoshone run on the colorado through glenwood canyon would also work. Its about 1-1.5 hrs to the east of grand junction. Its a short (1.6 mile) class III run that is roadside. You can hike or bike the shuttle along a riverside paved bike trail. You can lap it easily. Flows will be low, but if you want to get wet, it will suffice.
There is more flatwater on the colorado and on the gunnison, but these are your best bets. Only reason they are running is dam release.