Currently being upgraded to a proper rail trail, this section of abandoned railway line between Tonganah and Legerwood will soon be an excellent and easy ride for all riders as it weaves its way through some amazing cuttings, and contrasting forests.  Combined with occasional glimpses out over the valley below, and a bit of history lying on the side of the track this makes an excellent half day ride.
This route describes a circuit which allows you to explore the railway line, but also utilises some trails and the major (but infrequently trafficked) A3 Highway.

This ride ties together a couple of out and back rides to Grey Mountain and Pelverata Falls into a loop of sorts.   It is probably more for adventurous local riders  who don't mind some rough tracks and who are looking for a short bit of technical riding with some nice views at the end. 
However it can also make a great day out for less experienced riders just so long as you are willing to walk your bike a bit.  There are plenty of options to extend or shorten this ride for those looking for more or less hours in the saddle.

There is a dense network of trails criss-crossing the Kate Reed Reserve and it really is best enjoyed by pointing your wheel down the main trailhead and just exploring. For those looking to push themselves there are some dedicated tracks available and families with kids could equally enjoy riding down to the duck boarded area and having an explore.   Basically get in there and enjoy yourself.  This park has something for all levels.

The Clarence Mountain bike park is less than 10 minutes by car out of Hobart, and the 7km cross country trail provides a superb challenge for fit-intermediate riders and above.  For the rest of us mere mortals this park contains brutal sets of switchbacks that are sharp, steep, often rutted, and completely unforgiving.  If you're not sure of your skills I'd recommend the Glenorchy Mountain Bike Park over Clarence, but if you're up for the challenge … well here it is.

The Glenorchy Mountain Bike Park is only 15 minutes from the centre of Hobart and contains cross country, downhill and jumps courses.   The Park has the added advantage of being connected to the wider network of trails across Mt Wellington.  The route described here is a 5km cross country course, but this is only one of a growing network of trails that can be ridden in the park.