We stayed in Hathersage last June for a week without a car. Specifically chosen for its transport connections and walks.
Within the village itself, there was everything we needed - small supermarket, green grocer and butcher, 3 or 4 pubs that served meals and several other cafes and restaurants. The exception was an ATM. There wasn’t any way of obtaining cash with a ‘foreign’ card, and we did find a couple of cash only businesses. So would suggest bringing cash with you.
The public transport was quite good in theory. A train station and regular buses that run through the village. However the buses proved to be a bit unreliable and were infrequent on weekends. We did get stuck in Eyam one afternoon where the bus just didn’t turn up. After waiting several hours (and checking the live bus tracker which indicated nothing was imminent) we caught a taxi with another couple who were also stranded, although this took a while to come from a larger village. We were also unlucky on the day we were leaving as the train was cancelled as we sat at the platform. We were able to go back into town and catch a bus to Sheffield and resume our journey.
We really enjoyed our time in Hathersage. The walks were great and varied, the village, church and pubs are nice and the countryside is lovely in Spring. Bear in mind that Hathersage has a busy road running through it. Perhaps this is the case with a lot of English villages, but it was busier than I anticipated.