In winter, theatre is great. There are concerts at St. Psul's and St. Martin in the Fields.
Some of the smaller museums, like the Design Museum, the Postal Museum, the Dickens Museum, and the Victoria and Albert Museum of Childhood are also fun.
There are light displays at Kew Gardens and Kenwood House Gardens.
In summer, the gardens are great. You can visit the London Wetlands Centre, a Victorian reservoir turned wildlife preserve. The Olympic Park is also beautiful. Daytrips to Darwins house and Churchill's house are also fun.