Covent Garden's central piazza was London's main market from the 17th century until the fruit and vegetable trade moved south of the river in 1974. The Victorian market building now houses shops and restaurants, but the square retains its character as one of the better places in central London for street performance — the pitches are licensed and the standard varies from adequate to genuinely impressive.
The area around the piazza — Neal Street, Seven Dials, Floral Street — has a concentration of independent shops, specialist food stores, and the sort of mid-range and upmarket restaurants that make up the bulk of London's dining scene. The Royal Opera House sits on the northern edge; even if you're not attending a performance, you can sometimes walk through the public spaces during the day.
Nearest tube: Covent Garden (though it's a short walk from Leicester Square or Temple).