Hazelwell Park runs alongside the River Rea with National Cycle Route 5 passing straight through. It has a nice playground, ducks and bats at dusk when it's not too cold for them. The park is less lovely towards the southern end but if you keep on cycling along the route before long you'll hit the canal and be on your way to Stratford-Upon-Avon. If you decide to head towards town you can stop by for an ice cream, some art, boating and lots of caches in Canon Hill Park. We're hoping to do a small series of caches along this stretch of green :)
You're looking for a 7cm by 3cm magnetic key holder. The cache itself is a short walk away from Bournville Station and several bus routes.