The historic core of Barking — abbey, church, town hall, market — is compact and easy on foot, ten minutes end-to-end. Eastbury Manor House is about a mile east of the station; you can walk it in 20 minutes or take an EL1 or EL2 bus along Ripple Road.
For trips along the Thames or into the new Barking Riverside development to the south, the EL3 bus runs frequently, and a Thames Clipper river bus stops at the new Barking Riverside pier with services into central London. Cycling is straightforward on quiet residential streets but unpleasant on the A13.