I'd suggest the Strand Palace Hotel on the Strand. It's beside Trafalgar Square, Covent Garden (brilliant shopping) and slap bang in the middle of Theatre land, direct underground link via Piccadilly line from Heathrow at Leicester Square 5 mins away. Round London bus tours and Thames boat trip leave from the Embankment 5 mins away and the London Eye is 10mins away via the Millennium Bridge.