Table Mountain is the large volcanic plateau on the outskirts of town. It can be seen form almost everywhere in town and you can't miss it.
It is actually divided into two parts. The one with the large "O" is South Table Mountain. It is advised that people don't go up there without permission, as it is private land and there is a crazy guy up there who will shoot you with a beem bag.
The neighboring North Table Mountain contains an ecological reserve and is accessible to visitors. However, everything east of Cherokee Rd. is private, and there are some patches of private land that border the ecological reserve. The land is used for grazing cattle though, and no one actually lives up there, so no one will care if you trespass or not. There are a couple houses further, so if you see any don't walk by them.
From early December to mid April, vistors can get a look at some of the area's seasonal waterfalls. The most popular ones are Phantom Falls, Hollow Falls, and Fern Falls. There are about a dozen of them up there, but the rest are seldom visited. Some of the larger waterfalls also conrtain caves, and there is an abandoned mineshaft at Phantom.
The best time to visit is early March to mid April when the plateau is blanketed with miles of spring wildflowers.
There are no hiking trails anywhere, and it is very easy to get lost if you don't know the area, so it is recommended that vistors print out a good map, or go with someone who knows the area, and watch out for ravines and posion oak. They do offer free tours the first and third Saturday of each month during spring. It is advised that you not visit during the summer, as rattlesnakes are present, temperatures are really hot, and you won't see much anyways.
The best way to get there is to cross the Table Mountain Bridges over the Feather River, and take Cherokee Rd. You should pass the large sylicon mine.
For more information visit Wikipedia, and see the link below.