Oxford Street is the main shopping artery of London - ranging from incredibly tacky at it's eastern end (Tottenham Court Road tube) to a bit more upmarket at the western end (Between Bond Street and Marble Arch tubes). Bond Street (swanky luxury shops) and Regent Street (less swanky now) cross it perpendicularly, running down to St James (best for clothes shopping) and Piccadilly. All the big department stores cluster round Oxford Circus tube.
Nice areas: St Christopher's Place, north of Oxford St full of open-air restaurants and boutiques, and it's new rival Lancashire Place, off Bond Street itself are the places to eat. South Moulton Street for antiques and women's fashion. The fabulous Wallace Collection of pre-20th century art is housed in Manchester Square to the north of Oxford Street.
The wholesale garment trade is on the north side, between Oxford Circus and Tottenham Court Road. Soho is to the south of this area. The BBC is north of Oxford Circus and the area between it and Marble Arch to the west is full of great architecture and squares, not to mention Marylebone 'village' and famous Baker St (though there's nothing on it of interest except to Gerry Rafferty or Sherlock Holmes fans). The whole area is heaving late afternoons and all day Saturday. It's usually quicker to walk than take a bus at peak times. For a slightly quieter shopping experience, try Kensington High Street or Knightsbridge - served by the tubes stations of the same name.