Depends what you want. You can cycle anywhere in the forest, plus there are two forest trails, one of 4 miles (blue) and one of 7 (white). These are both suitable for any rider. They are both pleasant and they start and finish at the forest Cafe. As well as the forest cafe there's a cafe at the train station which is nice too.
If you want berms and switchbacks there's no continuous trail but there is what's called a skills area which has some short sections you can mess about on. You get to it off the white path. If you start from the visitors centre the skills area is on the left after you cross the road, identified by some signs and a rather steep, narrow drop down. Alternatively, go slightly past that and take the left forest road down. When it flattens out at the bottom there's a right turn up hill and when you reach the top there's a skills area on the left which is fun. You can also get to it quicker by cycling down Ashton road until you meet where the white path crosses the road and then go right.
If you want road cycling, then it's all good around there. Head down towards Beeston castle and around on the minor roads. You need OS 1:50,000 map No 117 to see the roads properly and any bridleways you may wish to take. On a road bike you can get into Wales quite easily as well.