This year has been an important one for domestic tourism with many Brits choosing to holiday at home, said the broadcaster.
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The Yorkshire episode on Monday shows the first summer season for the owners and staff of Whitby tourist attraction The Endeavour - a replica of Captain Cook’s ship.
Colin, dressed up as Captain Cook, tries to woo the customers, while the rest of the staff are rushed off their feet showing families the interactive sand pit and sea shanty karaoke, organising a curry night and welcoming 80 guests for Whitby Regatta.
"We meet the passionate Yorkshire team determined to make a success of the Captain Cook-themed Endeavour on its maiden summer," said the BBC.
"The team have survived some opposition to their new business from locals and owner Andrew Fiddler needs to get 150 visitors a day through the door to start making good on his investment.
"The programme follows Andrew and his 15 staff to see if they are able to stay afloat through the summer months.
-> 16 photos from the world premiere of BBC One sitcom ScarboroughCrowds packed Whitby harbour and canons sounded to welcome the Endeavour back to its spiritual "home" last summer.
The replica vessel made the journey along the coast from Middlesbrough to its new base.
It marked 250 years since Captain Cook, who began his sea-faring career in Whitby, set out on his epic first expedition to the Pacific in command of the Endeavour.
Owner Andrew Fiddler bought the ship at auction in autumn 2017 for £155,000, beating bids from Dubai, Portsmouth and London.
Watch the Great Staycation on BBC One Yorkshire and Lincolnshire at 7.30pm on Monday. People can also watch the whole series on BBC iPlayer.