May is a great time in the Lakes. We have a place in the north east, near Penrith, and one thing that I’d say is that it can take a long time to get around the lakes, so bear that in mind. I’d guess that Coniston to Buttermere would be well over an hour.
Nice walks near you
Around loughrigg, and you could case it for a ride at another time
Crinkle Crags and Bowfell from the three shires stone at the top of wrynose – fantastic walk, Bowfell is terrific
There’s a scramble up the front of Dow Crag, called easy gully I think, which is a much more interesting way up to the Old Man.
A bit further afield
Blencathra up sharp edge, and Helvellyn up striding edge are both great walks
Also up Whiteside from Crummock Water, over hopegill head and up onto crag hill, then down over wandope and whiteless pike.
Wainwright s are a great way to plan these.
Non walking you could try the steam yacht gondola on Coniston, and I’m sure that biketreks in Ambleside and wheelbase in staveley have demo bikes!
Have a good time