Mountain Resorts?
 

Our family of 4 is considering a stopover in the NC mtns for about 3/4 nights next August enroute to the SC coast.

We're interested in hiking, kayaking,bicycling, beautiful scenery, interesting towns and horseback riding.(preferably on-site or very close to our resort/inn)

Any recommendations? Thanks !

I'd begin in the Boone area. Banner Elk and other places are nearby.
Another would be the Asheville area. Where will yo be comiing from en route to SC.

This is a no brainer if you like horses....Cataloochee Ranch west of Asheville is fantastic. So is Clear Creek between Ashville and Boone.

Boone is a college town, and in my view not that picturesque, the small neighboring village/towns of Banner Elk and Blowing Rock are pretty although Blowing Rock can get crowded. There is much to do there, but I think better outdoor activities west of Asheville.

If you go towards Cataloochee, there is great rafting on the Nantahala, and for more advanced paddlers, the Chatooga. The Nantahala Outdoor Center is great for mid-level rafting, and if you get bored, Asheville (an hour) is very artsy, there's Biltmore House and Vineyards, and the waterfalls in the area coming down from the Blue Ridge are awesome. "The Sliding Rock" in Brevard, just below Asheville, is a natural wet rock slide of about 70 feet into a cold natural pool beneath the falls.

We did 4 days this spring up in that area, and it was a riot.

Hi Gretchen!
WE're travelling from central NJ.

The Swag Inn near Asheville. I haven't been yet, but I have friends who loved it.

The Grove Park Inn, in Asheville.

If you are coming from NJ you are adding a significant amount of driving to your trip. It can be pretty in NC, but the Virginia mountains are just as pretty and you would save hundreds of miles of driving.
But if you do want NC mountains, then the Boone/Blowing Rock/Banner Elk area is significantly closer than Asheville. And probably "higher".