Definietly worth a visit, great walks and a perfect opportunity to get back to nature. Some of the towns in and around the Yorkshire Moors are as follows:
Ampleforth - well knows for its Benedictine Monastery public school. The village over looks the Howardian Hills.
Brompton - a pretty little village which is set around a tiny lake. Locals argue that this was the birth place of flight as Sir George Cayley, a prolific inventor designed a glider some 50 years before the Wright Brothers. He also invented caterpiller tracks.
Cropton Forest - In the 1920's the Forrestry Commission created a large scale conifer plantation and now the area boasts one of the largest man made forests in the country. The woodlands, now fully matured now create over 100,000 tons of timber each year.
Danby - The National Park Visitor Centre is just half a mile which is a great base for anyone wanting to explore the wonders of this countryside location. Damby is a small but lovely village. One of those places if you blink you would miss it.
Guisborough - A local market town where weekly markets have been held for many years. A large 15th century church (St Nicholas) is worth a visit
There are many walks on the moors. Cleveland Way was the 2nd national trail in the UK. To walk it fully is 110 miles and its enirely within the North York Moors National Park. The walk is almost horseshoe U shaped. It starts in Helmsley, goes through Hambleton and Cleveland Hills to Urra Moor (its highest point). It then follows the coastal path to Filey Brigg. To make it a circular walk there is a section know as "the missing link" from Scarborough back to Helmsley.
For shorter walks you could try the crosses walk which is a hard going 53 miles circular walk starting at Goathland.