If you fancied a fairly relaxing weeks walking in Peak District, you could have a go at Derwent Valley Heritage walk.
It's 55 miles in total, as flat as any walk will be in Peak District...it follows the River Derwent through the Peak, and is easily breakable into 6 or 7 stages that you can get to by public transport...so you could stay somewhere like Chesterfield, and get to start of each stage by public transport each day, and get back to Chesterfield each day again via public transport.
In spite of it being flat, it features walking through some stunning scenery, walking through Chatsworth and Belper, for example are two highlights.
If weather or energies mean you don't fancy doing all the stages...easy to get on a train or bus for a day out at Manchester, Nottingham, Derby or Sheffield, etc.