There are so many places to visit close to North Mere but here are some suggestions for a couple of days of your stay:

Day 1 (in Kenilworth)

Morning walk across the fields to visit  Kenilworth Castle 

Lunch in the Old High Street at the  Virgins and Castle 

Afternoon use the augmented Kenilworth Revealed app to discover the secrets and stories of the Abbey of St Marys and wider Kenilworth history.

Day 2 (surrounding area)

Morning brunch in the Hatton Locks Cafe and see the famous stretch of 21 locks

Afternoon wander around historic Warwick