It is very central and much safer than people think. During the day Covent Garden is fun, with lots to see and plenty of cafes and places to eat. Notting Hill is great to have a relaxing drink and to meet new people. There is a market in Greenwich and if you really want to you can go to the Millennium Dome, but you better hurry before the end of the year. I know plenty of people that have been to Oxford for the day, only about an hour away and many tour companies offer it as a day trip.
Places are open later and the weather is generally warmer.
It's also nice to laze the parks and outdoors. Try and find out as much as you can about an area or venue before you go and take an umbrella. If you get a chance to try and visit other areas outside of London. London is very different to what the rest of the country is like, chances are, you'll come across somebody who is foreign rather then English.