SOAS university has a small gallery space dedicated to exhibitions about Asia, Africa and the Middle East. There's a small but beautiful Japanese zen garden on the rooftop (currently closed for refurbishment)
Ever since visiting the exhibition space, a few years ago, I don’t think I have ever missed one single show. It is one of the best exhibition spaces for contemporary art in London, in my opinion. The scale and the light feel right. The environment is not too overwhelming and not too small. In addition, the bookshop has a good selection of catalogues, art books and magazines.
Rotorino is a lovely little Italian, intimate but casual spot in East London. The food is great and when the weather is good - having your wine and pasta outside is nice.
On a hot day there is nothing better to do in London then go for a swim in the Heath ponds. You get completely transported you out of the city as Hampstead feels like being in the countryside except you're in central London?!