Getting Your Bearings
You can find this area on www.multimap.co.uk
Type NZ550275 into the location (postcode) box and click Find. This grid reference is centred on Teesmouth - you get a good overview at 50,000 scale.
Take Your Car
There's not much choice than to drive, though you could take a train to Seaton Carew and walk back to the Gare from there.