Chattanooga sits where the Cumberland Plateau meets ridge-and-valley country. That puts gorge hiking and ridge hiking within the same sixty minutes, and they ask different things of you.
Plateau hikes go down first. This matters more than people expect, because you do your climbing at the end, tired, and the descents are on sandstone that holds water. I have watched more than one person take a hard fall on a plateau trail in the first hour of a dry afternoon two days after rain.
Ridge hikes go up first and give you the view as a reward rather than as an opening. Lookout Mountain and Signal Mountain both have trail systems reachable from inside the city. Across the river gorge, Prentice Cooper has more mileage than most locals use and a road in that is worse than the map suggests.
The real constraint on all of this is parking, and it is not a minor logistical note. Several of these trailheads hold fewer than twenty cars. On a good Saturday they are full by eight thirty, the shoulder is now ticketed in more than one location, and a plan that assumes you will park where you intended is not a plan.
On gear, briefly, because I am asked. You need footwear with real tread and you need more water than the mileage suggests, because plateau humidity does not care what the thermometer says. You do not need most of the rest of it.
The finished guide will give measured distances, actual elevation gain, trailhead capacity, and a difficulty rating based on what the trail does rather than what the sign at the bottom claims.