there are a couple of spots to explore. Tamworth is a bit of a bike town. For sure take your bike, at the very least there are plenty of places to explore (ie, walking tracks to lookouts, camping areas etc. Make sure you have puncture protection though. Tamworth has some pretty viscious "jumping" cactus plants that I had many run ins with as a kid. Get some kind of tube tyre linner. Tubeless won't really cut it, nor will slime.