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.
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.