Easiest handicap accessible approach in US (sport/trad)

Tons of options as folks are already surfacing! If you're looking for a nice trip truly anywhere in the country, second Yosemite's Swan Slab Gully followed by the accessible path to Mirror Lake (drive-up with a parking placard!) and general Yosemite vibes. And.... get him on the wall with some adaptive support if he's interested!

gunks are the obvious east coast choice.  Bridge buttress at the new is another great spot. 

Sand Rock (specifically Holiday Block/West Side Block), but don't go too far out of your way for it

Bridge Buttress in the New isn't *quite* flat, but it's a 1 minute approach up a small number of stairs if that's doable.  What dad doesn't want to see his kid lead an inverted 5.12 offwidth?

Icicle buttress, icicle creek Leavenworth sits on the road. 5.6 to 5.10+ 

There is a 5.12 that hangs over the road not too far away from icicle buttress, and a 5.9 two pitch that starts from the ditch. Between the two features. 

I'll echo most of what others said. Will try to add a few specifics.

Southern California - Joshua Tree, especially Indian Cove, Echo Cove and the Hidden Valley Campground. We take folk with mobility challenges out here all the time.
- Spy Mountain. I wouldn't, but it fits the bill. Sport climbing in the Mojave. Jugs over Sand or the DMZ would both be fine.
- Big Rock. Climb where Lynn Hill learned to clip bolts!
- Stoney point? Just a feeling, idk... Never been.

Utah - Moab - Wall Street. Belay out of your car.
- Kanab has a crag at the entrance to town which fits the bill. Easy access but dinky climbs.

Nevada - Red Rock Canyon - Sandstone Quarry has a few crags that meet this description. Even a multipitch out of the parking lot.

Idaho - City of Rocks - Bath Rock, The Breadloaves, Elephant Rock, Parking Lot Rock, the list goes on...

Washington - Leavenworth's Icicle Creek Road. Icicle Buttress (As Kyle mentioned above), Barney's Rubble, Alphabet rock (not the most flat...)
-Potentially Index's Lower Town Wall. Has a few steps, but is a very short approach.
-Mazama - Fun Rock
-Vantage - The Feathers. Watch from your camp in the parking lot. Enjoyable and easy access side season camping.
- Mt. Erie - Some of the easy access climbing in the state. The summit is a parking lot, but it would definitely depend on your father's ability. The base of the walls would not be very accessible. The trail is not actually flat, but there are a few paved paths, and you could climb UP to him on the summit wall. Not my favorite rec.

Castle Rock in Boulder Canyon.

South Dakota Needles has some road-adjacent climbs.

Sport climbing at Rocky Face in North Carolina. 

Tuolumne has quite a number of easy to see climbs that fit your description. The first that come to mind are on Stately Pleasure Dome and Pywiak Dome.