In town: the old Guildhall, Town Hall Square, the market (the largest indoor market in Europe), the Lanes shopping area, the clocktower, the cathedral.
Out of town: Bradgate Park for some countryside and history.
Best Way To Get Around:
Walking is the best way to get around the city itself - the centre is compact and parking is expensive. Buses (0116 251 1411) and trains (08457 484950) will take you to the surrounding areas.