My husband and I traveled to Dartmoor last May - it was amazing! Definitely my favorite place in England thus far. We had a car and I was very glad to have it. We did the short hike to Scorhill stone circle and it is pure magic. Such an amazing feeling to be alone on the moor in an ancient stone circle. I'm not sure how we would have been able to reach the trail head using public transportation (maybe hire a driver in Chagford?) It was miles of driving on super narrow, twisty roads - lots of hedgerows covered in wildflowers, steep hills, and reversing to pull outs/pulling in the side mirrors/waving to folks in the passing cars. There are also a couple of clapper bridges nearby and a huge stone with a hole in it down the river a bit.
Ask the guy in the hardware store in Chagford for directions (you can also buy a map there - this tip is also in the RS England). There are also some great stores for picnic supplies in Chagford - a cheese monger who sells delicious meat pies and at least one bakery. We ate a lovely picnic lunch at Scorhill.
That night we stayed at the Edgemoor, had wonderful dinner there, and sampled some of the proprietor's extensive gin collection. We planned on driving a bit farther on from the hotel that evening for sunset on the moor, but I was exhausted from the narrow roads (it was my first day of driving on the left) so we stayed in, which was a definite mistake! The road opens up just beyond the hotel and you're right near Haytor and Hounds Tor. Plus - the Dartmoor ponies are there!!
We hiked up to the top of Hounds Tor in the morning. It's a short walk, but the views are amazing. My husband stumbled across a letterbox hidden at the top in one of the rock formations (without even knowing what it was - luckily I had read the RS guidebook :) We drove through the moor and stopped at Postbridge on the way out. We only stayed for one night, but I wish we had been able to stay longer.
Two extra fun facts - Hound of the Baskervilles is set on Dartmoor. I read it while we were there and highly recommend it (I love reading things set in the places I visit). And finally, in case you're a Bowie fan, the production design for the movie The Labyrinth was based on the Dartmoor landscape. Enjoy your trip! :) I'm so jealous!