Absolutely you should make the 30 minute drive to the coast.
Down at St Bees and south thereof down to and past Drigg there are gloriously sandy (and empty) beaches and great coastal walking. Using the rail service there are several linear walks possible.
At Whitehaven there is the Beacon Museum which tells the history of the town. That is down by the harbour which was once the 3rd most important harbour in England. The other museum is the Rum Museum which tells the story both of Rum production in the town but also the general trade with the Caribbean.
Also in the Beacon is the history of the tobacco and timber trade with Virginia.
Whitehaven also has the history of the John Paul Jones (founder of the American Navy) raid on the town. (If you go to SW Scotland visit his birthplace museum at Arbigland).
The forts at Whitehaven (captured by JPJ) were the only military installations in England to be captured by opposing forces during the American War of Independence.
Richard Wordsworth, a cousin of William Wordsworth (poet) was Collector of Customs at Whitehaven, and his very neglected gravestone is at St Nicholas' Church in the town centre- much more detail here- https://www.whitehavenparish.org.uk/about-us/st-nicholas-centre/guided-tour/the-wordsworth-connection.php
Also at St Nicholas' is the unknown grave and two memorials (also historic display) to Mildred Gale- whose grandson was the 1st American President, George Washington. St Nicholas' is open on Wednesday to Friday mornings and every 2nd Monday morning.
There is also St James' Church- a fine example of a Georgian Church.