To be honest Samantha, I would not advise Brixton as a place to go at night, except in a group. Daytime you should be fine, but as with most of London hang on to your bag! There is a nice arthouse cinema there and a fantastic gourmet vegetarian restaurant in a Church Crypt, the name of whcih escapes me. Bug Bar.
South Ken - museums, museums and more museums!
Great to see you are exploring different parts of London! Don't forget to check out Brick Lane/Spitalfields area too for markets and great curries!