If you want a hiking day trip head out anywhere in the Peak District. Favorites include: Edale, Hathersage, and Mam tor. Peak district is about 1-2 hours drive away.
Home of the bakewell tart, recommendation of the bride's mother. About one hour drive.
For somewhere closer and British. About 15-20 mins drive.
Nottingham castle and grounds is a fun trip in the city center. Stop by Ye Olde Trip To Jerusalem (oldest pub in England - contested) if you like an ale in a place that smells a bit like cheese in a cave.
Nice area to walk around with little house boats. One place you can get on them at Nottingham train station
Nice little walking park, right next to the venue.
Another nice walking area.