The Cumbria Wildlife Trust has suggestions for more good places to see birds and other wildlife.
Arnside and Silverdale AONB
The area to the south of Levens, around Arnside and Silverdale is designated as an Area of Outstanding Natural Beauty, and their website has suggestions for places to visit. Arnside and Silverdale are both pretty villages, and there are plenty of opportunities for gentle walks in woods and fields, with views across Morecambe Bay and the Kent estuary.
Most of the gardens that are open to visitors all year are attached to stately homes – see the Culture page. Holehird Gardens, near Windermere, is the home of the Lakeland Horticultural Society and its 17 acre garden is open to the public.
The area around Levens and southwards is limestone country, and you can walk from the cottage to Scout Scar to enjoy the flowers on the limestone grassland and views across the Lyth Valley (famous for its damsons). Whitbarrow is another good local walk.
More spectacular limestone scenery is found in the Yorkshire Dales. The village of Ingleton is a half-hour drive away – go there for the waterfalls trail (which includes a nice unconformity at Thornton Force for anyone interested in geology), or to climb Ingleborough. For the very energetic there is the Yorkshire Three Peaks walk (Pen-y-ghent, Whernside and Ingleborough – 24 miles, 5,200 ft of up, and usually starting from Horton in Ribblesdale).
A little further away (another half hour from Ingleton) is Malham Cove, topped with a large area of limestone pavement.