There are numerous firetrails and a bit of single track throughout the Meehan range. Most people start at the carpark on Belbins road. To get there take the Cambridge turn off from the highway and then take the first left and follow that to the end. Ride along the firetrail and follow your nose. There is a nice single track that parallels the fire trail on the right hand side. If you keep following the trail you will eventually come to a large steep hill. Push up this to the ridge. If you go right from here you will head up towards Rocky Tom. If you go left you can follow the ridge along and take several different downhills down towards the highway. Most of them finish in the vicinity of Grassy Valley. From there take a single track that follows the highway back around towards the carpark.
Grassy Valley is a well developed dirt jumps area. You can find it just off the highway to the east of the Mornington/Warrane turn off. See http://www.grassyvalley.com
There are some OK XC firetrails at the Risdon Brook dam. There is also a XC track in Risdon Vale itself - directions?
There is a downhill track over at tranmere. Check out tranmere map.pdf for how to get there.
There is a large network of cross country trails around South Arm, called the Tangara trail. This is one of the best easy cross country areas around Hobart. Check out the map link below, and make your own circuit out of the various trails. http://www.ccc.tas.gov.au/webdata/resources/files/tang2.pdf