For one night in London I'd certainly not go to theatre, especially if you've never been to London.
Instead, once you've dropped your luggage take the hotel's free shuttle back to Heathrow. Follow signage to the Heathrow Express. Use your debit card to purchase roundtrip fares. Board the train and in 15 minutes you will arrive at Paddington Station. Go to the Ticket office and get your paper Travelcards so you can use the Tube.
From Paddington Station you are going to take Underground (Tube) train via the Bakerloo (Brown) Line to Baker Street (Enjoy the Sherlock Holmes tiles) and hop on a Jubilee Line Tube Train ( Grey) and take it to Westminster Station. Exit (Mind The Gap) and walk out into Parliament Square and see iconic London.
From here you can choose to walk up Whitehall to Trafalgar Square or walk up Birdcage Walk through St James Park to see Buckingham Palace. Depends on daylight and your choice of what it is you wish to see. You could also leave Parliament Square and walk over the Thames via Westminster Bridge and ride the London Eye.
Personally I'd walk up Whitehall past the Horse Guards and #10 Downing Street to Trafalgar Square (Lord Nelson's Column, the Lions, National Gallery) up past St Martin's of the Fields toward Leicester Square then head on over to Covent Gardens for dinner. Or if you simply want to keep exploring instead of heading to Covent Garden walk a bit further and turn Left on Shaftesbury and head toward the bright neon of Piccadilly Circus and into SoHo for dinner. You can plan your walking routes by looking at Google Maps Satellite view.
Then hop on the tube and head back to your hotel.
Enjoy your evening in London!