I went to Clumber Park on Sunday. You have to book a half hour time slot to arrive, and there are limited spaces, but can stay as long as you like. This is at the cost of £5 per adult, National Trust members get in free. I arrived at 12:30. There was around 5 minutes of queuing to get in. Once we got parked (plenty of space on the big field) it was easy to avoid the crowds as the place is huge, but there were admittedly more people crowded around the main buildings / cafe and there was about a 10 to 15 minute queue for the toilets. Most people seemed to be adhering to social distancing / face masks inside though. Can't comment on Rother Valley Park. Similarly went to Bakewell the weekend prior, not with the intention of going into the town centre though. We got a free parking space on the road but I think that was lucky. The car parks looked chock a block but I think there were still spaces. We did a round walk circling the area and didn't come across too many people. Sheffield Round Walk is a good shout. If planning to do the whole route though it would be wise to plan food / toilet breaks around what is and isn't open at the moment. I know the public facilities at Endcliffe Park are now open. Pre-lockdown it was easy enough to pop into a pub / cafe along the route for refreshments etc. maybe not as easy now.