Two of my favourite galleries are both down Trafalgar Street. These are RareKind and OContemporary. Together, they span the two ends of the contemporary art scene.
RareKind. This place specialises in urban street art and grafitti. Downstairs is a small space with works by various "graf" type artists. I have seen pieces by local boy Req in there and currently they have some pieces by Jimi Crayon. Pieces are available for sale and they do commissions as well. Upstairs is a record shop specialising in Hip Hop, especially the UK variety. I like this gallery as it shows how good some of the graffiti out there can be. It all seems reasonably priced as well.
OContemporary. At the other end of the scale is OContemporary. This one is a big bright space full of pictures from your favourite contemporary artists. They have pieces by Andy Warhol and Bridget Riley as well as more modern artists like Tracey Emin and Takashi Murakami. They also have regular exhibitions of up and coming artists. This gallery is good as it gives Brighton a solid set of work (albeit prints) from proper famous artists. It is also a good barometer of who is on the way up in the art world. Sometimes it is hard to tell just what is their current exhibition and what is part of their collection. Presumably the ones piled up against the back wall are in their collection. :)