The 'Mystery Hotels' are just ordinary ones. It just saves them having to specify a particular hotel which may be fully booked. National Coaches have contracts with entire groups of hotels and just use as many as necessary on a particular day. I booked a London show and hotel trip several years ago. The Hotel was one I had never heard of but was perfectly acceptable,with a clean bed and full cooked breakfast. Did you know there are over 2000 hotels in London?
I can't help directly with your question but I spent a few days interviewing footpath users in Folkestone and ended up talking to dozens of people who were holidaying with National coach holidays at the Grand Burstin Hotel there. Every one of them had nothing but praise for the company. (I've stayed at that hotel myself. If it's indicative of the general standard of hotels used by National coach holidays then I'd certainly have no hesitation in booking with them).
I was so impressed that I did some research about the company (mainly in the hope of finding out if they operate tours from my part of the country - unfortunately they don't). It quickly became obvious though that they've got a very big contract with Britannia Hotels. So the 'mystery' hotel could well turn out to be one of these:
https://www.britanniahotels.com/hotels/the-britannia-hampstead-hotel
If National Holidays don't run from your area you could try looking on the Shearing site as they are part of the same company and often use the same type of hotels.
Off topic, but a few (quite a few) years ago my friend's grandparents were on holiday in Hastings, East Sussex. One day they booked a "mystery" coach trip for the day. They finished up in the delightful town of Royal Tunbridge Wells, Kent. Er...where they lived!
They popped indoors, had a cup of tea, checked the post and rejoined the coach for their return trip to Hastings :-)