There is plenty of two-hour parking in town. From town walk north on Bridge Street (and Applachian Trail) to cross the bridge over the French Broad River. Stay on the right side of the bridge. Immediately after crossing the river, there will be a guard rail with a path to the street below. Follow that street up river about 50 yards until you cross a wooden bridge. Continue along the river and you will see white blazes marking the Appalachian Trail every 100 feet or so. After a few hundred yards, just beyond Surprise Falls, a beautiful rapid on the river, the trail goes away from the river with several switch-backs upward. The trail is well marked and well established.
There are three large rock promontories along the way with great views of the river, the valley and town. Lover's Leap is the second rock outcropping (be careful walking out the edge!). After the third outcropping, take a left from the Appalachian Trail (you will see a white arrow on a rock showing the Appalachian Trail going up hill). To loop back to the parking lot, keep walking downhill on the trail that branches to left. This will take you back to the Appalachian Trail and retrace your steps to town.
For a longer hike, continue on the Applachian Trail to Tanyard Gap (where the trail crosses US Highway 25-70 east about 3 miles by car). It's a challenging uphill hike of 5.9 miles. If you have two cars, you could leave one in Hot Springs and drive to Tanyard Gap and hike downhill for 5.9 miles. Or reverse for a good challenge.
