OOh you are staying in a fantastic area Covent Garden - handy for everything really - sightseeing wise Covent Garden itself (for sightseeing/shopping/dining), Picaddilly Circus if you walk one way, and Leicester Square and Trafalgar Square if you walk the other with Embankment and Houses of Parlaiment and Big Ben beyond.
Sightseeing hop on the tube to:
St James Park Tube for Buckingham Palace,
Gloucester Road for Natural History Museum, Embankment/Westminster for Houses of Parlaiment and Big Ben,
Tower Hill for the Tower of London,
Regents Park for London Zoo.
Hyde Park Corner for Hyde Park
St Pauls for St Paul's Cathedral
Shopping wise - Oxford Street/Regent Street/Covent Garden,
Sloane Square on the District or Circle line west bound for Kings Road - fantastic shops.
High Street Kensington for Kensington High Road - full of shops there. Knightsbridge for Harrods,
Camden Town on the Northern Line for Camden Market,
Notting Hill Gate for Portobello Road (Camden and Portobello offer quirky shops and market stalls for unique stuff.
Of course don't forget stuff like the London Eye, Tower Bridge, Boat Rides on the Thames, Open Top Buses to catch everything in one go etc etc gosh I could go on and on - I hope you fit loads in and enjoy your visit!!