I know the Rock trail is indeed open (Newberry Rd, west of I-75). Though I have not been there myself, friends of mine have been there recently and they go there often, speaking very highly of it.
There's also the Powerlines trails, a network of random stuff in NW Gainesville. From my knowledge, the easiest way to get there is take NW 23rd st and head west, past I-75 and keep going until the road becomes a dirt road. The trails will be shooting off from there.
For an easier, more in-town ride, there are the Creekside trails and the 8th ave trails. The Creekside trails start from the parking lot of the Creekside trip mall on 2nd ave (near the intersection of 34th and University ave.) Look for Calico jacks, it's in the back of that parkinglot half way between the CJ's buildings and the other set of buildings to the right. it's a few miles of singletrack, nothing too technical but a nice ride nonetheless.
The 8th Ave trails start at the Lobololly nature park, which is on 34th St just a bit north of Unviersity Ave. There, you can find some singletrack shooting off the main path. There's even a little bowl with some jumps (and it;s been dry the last few days so you can actualy ride in it!) After you get to 8th st (you'll see the park directly across), cross over no the north side of the street and head a little east for the next section of the trail (you can't miss it). More singletrack that is preety fun if it's dry.
There's also some stuff in the SE portion of town by Bivens Arm and the Sweetwater Preserve. Also something called the Split Rock trail off the south side of 20th Ave just west of I-75.