For a relaxing place for tea (and great pastry) in the Old Compton gayborhood, try Maison Bertaux on Greek St, 1/2 block down from Old Compton.
Walking Tours? Have enjoyed a number from London Walks ( http://londonwalks.com/
) - led by very knowledgeable guides. Have enjoyed the nighttime Jack-The-Ripper walk, one in the canal area, and one including a boat trip down the Thames to Greenwich with a tour of the observatory area.
Hampton Court is worth some time.
For the outdoors, try Kew gardens. If you go to Kew, there is a great tea/lunch spot between the tube stop and the garden entrance. Regent's Park, including Queen Mary's Rose gardens, which should be in bloom.
For food - try Mon Plasir, 21 Monmouth St (near theaters). Small french restaurant with excellent food (I'm not a fan of English food).