If you want a longer walk, head up towards the pool and keep going. After a short while, you'll get to the edge of the pool, and a bend in the road. There's a yellow footpath sign here, on the left, head through onto the path. A little way in, you'll see a track through the meadow leading up to the wood. It's nice to take this, and wander around the edge of the wood until you hit the track again. Or you can go straight on. In fact, go straight on is the key phrase here, as eventually you'll reach Newtown Linford, which has 3 cafes, and , if you turn left as you exit the footpath, there's a pub called The Bradgate further up on the right. 
And, of course, the main attraction, Bradgate Park, which you enter though the car park, feeling smug as you see that you've avoided paying for parking. 
Remember you have to walk back too!