It's been a few years since I've stayed there, so FWIW. There was a nice park on the south end of town.
Arches National Park is a must see. Colorado National Monument is east an hours drive toward Fruita, CO. La Salle mountains.
Here is a good site for info.
You don't say when you are going. There are some local events; Melon Days in Green River, they every kind of Melon you can imagine. Palisade CO peaches, best I've had anywhere. Wineries there, too.
Driving: It is a two lane road across the desert south bound which falls into Moab at the Colorado River. Traffic is impatient. Continuing south it is up hill 25 or 30 miles with a few steep spots. If you go in summer it will test your cooling system and driving technique.
Have you been to Monument Valley? Continue South through Bluff, two RV campgrounds and cross the river at Mexican Hat, have lunch.dinner at the Swinging Grill. MV is hour or two to the west. If you go east there is 4 corners.
Enjoy the drive!