Thanks for the replies, and I hope this thread continues. There are a host of good places to visit, both at home and overseas. Yes, I live in such a destination place; Grand Junction has the
under-appreciated Colorado Riverfront Trail from Fruita to Grand Junction and most of the way to Palisade.

Steve Carter, on Flickr
and the Colorado National Monument, which is very bicycle friendly (on Saturday morning you're likely to find more cyclists than cars on the road) and a host of paved county roads which can be really beautiful at the right time of day [i.e. not so much in the late afternoon when it's hot and the schools let out!]. Fruita has successfully positioned itself as Moab East, with a good number of road and mountain biking choices, several good bike shops and restaurants, brewpubs and coffee shops.
Then there's Glenwood Springs, which has two five-star trails,
Glenwood Canyon bike path and the
Rio Grande Trail which follows the route of the D&RGW to Aspen:
IMG_20170727_144755152 Steve Carter on Flickr
One of the joys of taking my bike has been discovering local gems which the locals don't really appreciate, in places like Iowa, which until now for me has been merely a progression of interchanges on I-80. Who would have imagined, for instance, that the people in Des Moines can enjoy a trip every full moon along the High Trestle Trail with stops at every one of the many trailside taverns along the way?
Steve Carter on Flickr
Please add your own local recommendations to this thread!