I can see the OP has updated to say she has put off her visit till next week. I very much doubt the situation will be any different then.
We live in a National Park and have similar concerns to the good people of Whitby, other coastal communities and National Parks. At this time, local residents don't want visitors, local businesses don't want visitors, local police don't want visitors, local mountain rescue and RNLI don't want visitors, local councils don't want visitors, local minor injuries units and hospitals don't want visitors, local tourist boards don't want visitors, local National Park Authorities don't want visitors, and so on. Loos, cafes, restaurants, pubs, attractions and many car parks are closed. The Scottish, Welsh and Northern Irish governments don't want visitors. Notice any pattern here? If so, please take the hint and respect the serious concerns of local communities and services. Why go where and when you are not welcome, when waiting a little while longer until you are will make all the difference to how you are received and to helping to control viral spread for every single one of us?
The only people saying go are the UK government, well, the English part of it. Boris is out of step here. He has got this wrong. I would have more respect for him if he recognised this and put a 5 mile, postcode or county travel limit in place for exercise, except for those few with medical exemption as before. At the moment it just looks like a shambles, causing untold worry and division, and inviting a second wave. It's the ill-fated herd immunity policy once again, by the back door.
My family miss the sea and coast dreadfully, spending up to 13 weeks a year there at the very best of times, and even an afternoon would seem like a huge treat now - but we will not be going until it is safe to do so, until we are welcome, and until we can contribute to the local economy. We respect the feelings and fears of locals, just as we would like people to respect ours here in our National Park. We might have the right to travel for exercise from today, but we have the responsibility to stay local.
For those who feel their wanting and right to travel to exercise trumps all, at the very least don't go in the local shops or petrol stations, don't park or walk around the towns and villages where people including many elderly and vulnerable live, don't light fires or BBQs, don't sit there with your engine running adding to air pollution, take your litter, nappies and dog poo home, and avoid the honey pots.