From Downtown Chattanooga:

From Downtown Chattanooga, take US 27 North over the Tennessee River and travel 1-2 miles to the Signal Mountain Road exit (U.S. 127 North). Turn right toward Signal Mountain.  At the base of Signal Mountain, at the intersection of U.S. 127 North and Highway 27 West, turn left onto Highway 27 (Suck Creek Road…this will be right across the street from Subway).
 
Travel exactly 4 miles on Suck Creek Road.  After you pass “The Little Store” on your left, you will take the next left onto River Canyon Road. There is no road sign here.  Travel on this road for many windy miles (30-45 minutes depending on your pace) – always keeping the river on your left.  You could stop at the Pot Point Cabin, which is located 4 miles down River Canyon Road (on your left).  Take in the view of the river from this beautiful spot.  The Tennessee River Gorge Trust owns the cabin, and as long as it is not rented, you would be welcome to park and take a look around.  There is also a self-guided nature trail located on this site (the trail head is located by the parking area across the street from the cabin).  Hikers are welcome at any time, although fall through spring is the nicest time to hike the trail.  There are many chiggers and ticks during the summer months. 

Shortly after the cabin, Suck Creek Road becomes Mullins Cove Road.  Continue until you get to E. Valley Road (State 27).  Turn left. 
 
Take a left onto Highway 41 and this will bring you back towards Chattanooga.  Travel 15-20 minutes and (if you have time) take a detour to TVA’s Pumped Storage Facility at Raccoon Mountain.  It is a site to behold, and there are great views of Chattanooga and the River Gorge from several of the scenic overlooks.  You could easily leave an hour or two to drive around this impressive compound and get a number of pictures of the Gorge. 
 
App. 2 miles after the Pumped Storage Facility, you will come to I-24.  You can either go west toward Nashville or east toward Downtown Chattanooga.