To show your appreciation of history and culture, take a tour of the Royal Pavilion:
http://www.royalpavilion.org.uk/
For individual shops, head for North Laine:
http://www.visitbrighton.com/interests__themes /brightons_villages/34.asp
For a great selection of 'ethnic' restaurants (many of which only open at night) try the area around Preston Street. (The Viceroy of India, on Preston Street, is one of the best Indian restaurants I've ever been to).
Norman's (apparently homophobic) response to your question points out that Brighton is popular with the gay community. As Norman would discover (if he only had the courage to try), some of the best bars and restaurants are often to be found in the (nominally) gay areas of British cities. In Brighton, that means heading for Kemp Town.
Chris