- all paved
- no cars
- safe
- low crime
- nice views of nature
- small towns
- 200-mile route
- 32mm tires
- USA
Gonna have to compromise on something. 
An improved surface but not technically 'paved' trail can be fine. On the crushed&packed stone Mickelson Trail in the Black Hills, I saw folks riding everything from fat bikes to road racers with 21mm tires.
Rather than a linear tour, consider 'star touring', where you establish a base camp and ride out in a different direction every day.
Also, don't overlook urban trail systems. From my house here in Parts Unknown, I can ride away 100 miles and have 72 of them on paved trails. Denver has an extensive system.
Speaking of Colorado, a ride from Keystone to Glenwood Springs (paths & quiet roads) would be memorable for your family.