The Design Museum is a museum in Kensington, next to Holland Park, which covers product, industrial, graphic, fashion and architectural design. There is also a nice cafe on the 1st floor with beautiful views of the park.
I only made my first visit to Troy Bar fairly recently but it's already become a Friday night regular, and I feel like I've wasted a lot of nights not being here. Caribbean food, 4 Red Stripe for a tenner, an incredible house jazz band and as good an atmosphere as you'll find in the city.
London has great green spaces. There are large royal parks and small public gardens, hidden allotments and roof terraces. Each one has its own identity and characteristics and everyone has their favourite. In summer they become extensions of people homes, you see girls sunbathing from 9 am and the endless picnics mean you can eat 3 meals a day in the park. My favourites - St James Piccadilly Gardens, Hyde Park, Barbican Conservatory.