Cache creek ( near Jackson) is a nice ride, You can go as far as you want, But it's mostly an out and back trail. Unless somebody moves your trailer.
I usually camp down on Granite Creek. There are several trail heads by the Granite Creek Hot springs. One of which goes up to Torquoise Lake and down Cache Creek. You can also just wander the area around Granite, up and over into Shoal Creek or go up Jacks Creek.
South of the Hoback Hiway is lots of riding if you go down the Cliff Creek road. Too far away to see the tetons, But pretty riding still.
This is looking into Shoal Creek in October during a deer hunt and rain storm. But as you can see, it's pretty open and easy to meander thru
This is Granite Creek and you can see the trail down by the river
Heading up Granite Creek
My Daughter heading down the hill, You cross the river below the falls and climb up that trail on the opposite side.
The trail up Granite Creek does have some rocky sections But most is not too bad
Probably the most stunning ride is the Idaho side of the Tetons. Come in from Tetonia ID into Granite Basin.