Stanmer is easily reached by public transport:

BUS: Brighton & Hove services 25, 23 or 50 run frequently from Brighton to the Universities, stopping at Lower Lodges. B&H services 28 and 29 run frequently from Brighton and from Lewes. From April 2015 the 78 bus runs hourly from Brighton station all the way into Stanmer village. It is FREE to use the bus within the park, or you can get the bus from Brighton and leave your car at home.

TRAIN: Frequent train services from Brighton and Lewes to Falmer station and through the subway under A270. 
Cycle and foot: There are good cycle paths to Stanmer from Brighton and from Lewes, and footways for pedestrians. 
CAR: There is limited parking within the park. Please don't park on the grass or in the residents' area, and please park considerately: make sure it's not you that is responsible for the 78 bus service being suspended because of obstruction.

Stanmer Park