Shamrock, Tx also has a lot of old 66 atmosphere. The U Drop Inn gas station has original restored gas station pumps, a visitor info station and a replica of the old stone Texas shaped markers that once welcomed you as you entered the state.
When you're "standin on a corner in Winslow, Arizona" there's a mural painted on a wall of the girl in a flatbed Ford from the Eagles song, and the 66 road sign in the intersection, plus a great shop of 66 memorabilia souvenirs.
Petrified Forest NP and Painted Desert has a 66 monument, and one of the old Harvey Hotels, the Painted Desert Inn, beautifully restored now used as a little museum.
As you drive along I-40, you'll see the old 66 pavement alongside in some places, weeds growing through.
No reason you can't take a trailer. In fact, there's a marker about 66 in Santa Fe on the sidewalk in front of the historic Trailer Ranch RV Park.