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 app. 15 miles until you get to E. Valley Road (State 27)...there is no road sign for E. Valley Road, but it is located just beyond Ebeneezer Presbyterian Church.  Turn left. 
 
Follow E. Valley Road until you come to Highway 41.  Cross Highway 41 and stay straight ahead until you come to I-24.  Go under the interstate and turn left.  Then take I-24 East.  Once you cross Nickajack Lake, you can either remain on the I-24 and follow the signs to Chattanooga, or exit onto Highway 41 (Haletown).  If you take Highway 41, turn left at the top of the exit ramp and remain on Highway 41 for the scenic route.  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.