Chattanooga was a pretty well fortified city during the war (I suggest you check out Cities Under the Gun: Images of Occupied Nashville and Chattanooga by James A. Hoobler for period photos). In the intervening 145 years though most of these entrenchments have been replaced with buildings. A few signs, which are usually pretty hard to find, are around to show where forts used to be. The best marked is a spot for Fort Wood. There is no interpretive markers here, just a very large gun pointing towards Missionary Ridge.
There is also apparently a park on Cameron Hill (on west side of downtown) but every time I've tried to get there a variety of construction projects kept me away.