Yes I do have a mountain bike - it is around 15plus years old, so does not have any suspension and is great fun on really rocky paths and muddy single-track. Unfortunately here in the flatlands of East Anglia there are not too many places where it is really needed. I have taken it up to Thetford Forest, there are some great swooping tracks through the forest and it has been up to the Lake District a few times, but the big knobbly tyres are not so much fun on tarmac, they seem to soak up the pedaling energy.
What I generally do is mentally map out an area that I want to cycle around and roughly how far and how long it will take. At the moment I always carry lights with me. Even when I expect to arrive back in the light it does not take much to change my plans. One day I had three punctures and ended up having to take part in a conference call sitting on a bench in the middle of Burwell because I was not able to get back home in time. I am not sure what the locals thought of me, but at least there was cell-phone coverage and it was not raining. Cycling on a bicycle is much more comfortable than spending two hours sitting on a wooden bench though.
On the way round I then look at the map on the GPS to see if there are any interesting byways. It always surprises me how many byways and BOATS I pass. (Where BOATS means Byways Open To All Traffic - a UK legal term!). If the byway is roughly in the right direction or quite long and not too rutted then I head down it. Sometimes I end up turning around, most times I find myself in the middle of the countryside, away from traffic just pedalling. Here is one such track that seemed to be popular with the local horsey fraternity, well I saw one horse and rider. It actually shortened my planned route and the track included its own bridge across the M11.
Farther around my route I detoured through Fen Drayton along a "no through road" to find that it ended up in an RSPB reserve at Fen Drayton. (http://www.rspb.org.uk/reserves/guide/f/fendraytonlakes/directions.asp) Just off the Sustrans Route 51, the only downside is that they are building a guided busway through the area (Cambridge to St Ives) and so the tracks were being used by heavy lorries. The lakes are man-made from excavations for gravel/sand and so have "roads" that are able to take the heavy traffic. and to be fair I only passed three trucks. Here are some birds!
I also detoured to another village - Conington I really like the shape of the church there, as seen here silhouetted against the sky. (http://www.honeyhill.org/cthi.html for a history of the church which dates from the 14th century).