Robin Hoods Bay is easy to access by car and by public transport.
There is a regular bus service from Scarborough through to Middlesborough which calls at Robin Hoods Bay, Whitby and Runswick Bay on the way. In the summertime it runs every 20 minutes or so. X93 bus timetable
If you are planning on coming by car, essentially if coming from either North, South or West, once on the A171 follow signs for Whitby then Robin Hoods Bay is signposted.
Trains from the South and West come in to Scarborough Station with changes from the South generally at York or Leeds. Trains from the North come in to Whitby Station. Please see National Rail for more information and help in planning your journey.
There are several regional airports but all are some distance from Robin Hood's Bay. So you will need to hire a car or use public transport to complete your journey. All airports are well served by both buses, trains and metro's.