My favorite "first" introduction to London (been there a half dozen times, have taken a number of people on their "first" tour) is a long walk, hitting the core of London.
It comprises some of two or three Rick Steves walking tours found in his London book.
I like to start by getting off at the Westminster underground station, and as you exit, you are hit by Big Ben right in front of you, there is a handy pub right there, St Stephens Tavern, where you can have a pint and take in the view. From there, basically do the "Westminster Walk", taking in the Parliament building, the Abbey, and heading up Whitehall to Trafalgar.
From there, head towards St Martin in the Field, and nearby is another great pub, the Harp, where you can try some craft English ales, then head towards Covent Garden. From there head to the Strand, where you can pick up Ricks City Walk for a while, up to St Paul's. There are a couple other great pubs along the way, Ye Olde Cheshire Cheese for one, but stops will depend on how fast you walk, and your taste for beer.
Cross over the river on the Millennium Bridge, and wander down river to the Borough Market area. You can pick out items on Ricks Bankside Walk along the way, ending up at London Bridge. The George is another historic pub up that way. You can continue up to Tower Bridge and a view of the Tower, then find a station to head home, or maybe up to SoHo to find a good restaurant.
The long walk is good for jetlag, you get a few pints, and can work in a nice meal before heading back for a deep sleep.