24 hours in London

If you'd like to see some theatre your first stop should be the 1/2 ticket booth in Leicester Square. Then you'll be able to pace yourself for the rest of the day knowing you have theatre to attend that evening. Globe tickets are not at the half price booth. thoe you can reserve onlne if any are left for this season. If you wish to remain outside and not confined to a museum then visit the Camden Lock Market. From there walk along the canal path crossing over into Regent Park, passing by the London Zoo. Might also Check to see whats on at the open air theatre. http://openairtheatre.com/. Or visit Spittafields and Brick Lane markets or enjoy a walking tour of street art in the same area. http://www.freetoursbyfoot.com/london-tours/tour-calendar.

Shakespeare's Globe tickets aren't always (and maybe not ever?) available at the half-price ticket booth. If you know that that's the play you want to see, it's not too early to go to their website and buy your ticket now.

For what it's worth, I saw Pericles last month at the Sam Wanamaker Playhouse, the Globe's indoor 17th-century style theater, and loved it. We got our tickets two months in advance, and by the day of the performance it had been sold out for a long time.

Globe tickets are on sale now and I would agree that you need to book immediately. Most Shakespeare performances at the Globe sell out well in advance nowadays.

Claudia has the right idea. We did enjoy the imperial War Museum. The Tate Modern is well worth it. Covent Garden is mostly commercial shops and street performers (Touristy). Camden Lock is a real street market. St Paul's is more fun for two, so you can do the whispering across the dome. Go to Threadneedle St in the financial district which is closed on Sunday. It's the only day you can stand in the street and look up at the fabulous facades of the Banks. There are a few pubs here that are in former banks that have kept the décor...stop in for a pint.

Since you'll be at the Globe, you should check out Borough Market. Walk east from the Globe, along the south bank for about 8 or 9 blocks, then turn south onto either Stoney Street, or Cathedral Street. If you walk down Cathedral Street, you will walk right past Southwark Cathedral, also worth a pop inside to see. Borough Market is blocks and blocks of vendors with fruit and vegetable stands, their own farm products, such as cheese (ask for small samples), and baked goods, such as muffins and cake. You will find bakeries, coffee shops, sandwich shops, cafes and restaurants. A great place to walk around for an hour and to grab a bite to eat.

Borough Market is interesting, but is closed on Sundays.

Realistically, if your flight is on time, you will be at your hotel just after noon. The Eurostar is quicker door to door. Paddington is not close to any of your proposed attractions, so it will be the best part of 1 pm at your first destination.

Due to your limited time in London, to save time, you should spend focus on one geographical area such as Kensington (Palace/ museums) or the City (St Pauls/Globe etc). St Pauls has more limitations on opening on Sundays due to services being held. Most London theatres are closed Sunday night, but the Globe is open with performances, usually at 7 pm. So, assuming you can get tickets, that gives you less than 6 hours during which you will need to eat 2 meals. Book Globe tickets well in advance.

Covent Garden is mostly national multiples these days rather than independent traders, but it remains very touristy. Camden Market gets busy these days at the weekend, with restrictions on tube access due to the crowds. The street food here is good.

A 3 hour check in is recommended for your return flight, particularly with the heightened airport security at present., so you will have an early start.

For what it's worth, here is what the New York Times writer would do in 36 hours:
http://www.nytimes.com/2008/04/20/travel/20hours.html

That said, my preference is to wonder about town enjoying its ambiance while seeing and experiencing a couple if check off the list thing. Here's RS' list in part:

At a Glance
▲▲▲ Westminster Abbey Britain's finest church and the site of royal coronations and burials since 1066.
▲▲▲ Churchill War Rooms Underground WWII headquarters of Churchill's war effort.
▲▲▲ National Gallery Remarkable collection of European paintings (1250–1900), including Leonardo, Botticelli, Velázquez, Rembrandt, Turner, Van Gogh, and the Impressionists.
▲▲▲ British Museum The world's greatest collection of artifacts of Western civilization, including the Rosetta Stone and the Parthenon's Elgin Marbles.
▲▲▲ British Library Fascinating collection of the most important literary treasures of the Western world.
▲▲▲ St. Paul's Cathedral The main cathedral of the Anglican Church, designed by Christopher Wren, with a climbable dome and daily evensong services.
▲▲▲ Tower of London Historic castle, palace, and prison housing the crown jewels and a witty band of Beefeaters.
▲▲▲ Victoria and Albert Museum The best collection of decorative arts anywhere.
▲▲ Houses of Parliament London's Neo-Gothic landmark, famous for Big Ben and occupied by the Houses of Lords and Commons.
▲▲ Trafalgar Square The heart of London, where Westminster, The City, and the West End meet.
▲▲ National Portrait Gallery A Who's Who of British history, featuring portraits of this nation's most important historical figures.
▲▲ Covent Garden Vibrant people-watching zone with shops, cafés, street musicians, and an iron-and-glass arcade that once hosted a produce market.
▲▲ Changing of the Guard at Buckingham Palace Hour-long spectacle at Britain's royal residence.
▲▲ London Eye Enormous observation wheel, dominating — and offering commanding views over — London's skyline.
▲▲ Imperial War Museum Exhibits examining the military history of the bloody 20th century.
▲▲ Tate Modern Works by Monet, Matisse, Dalí, Picasso, and Warhol displayed in a converted powerhouse.
▲▲ Shakespeare's Globe Timbered, thatched-roofed reconstruction of the Bard's original "wooden O."
▲▲ Tate Britain Collection of British painting from the 16th century through modern times, including works by William Blake, the Pre-Raphaelites, and J. M. W. Turner.
▲▲ Wallace Collection One of the finest private family art collections anywhere — free and open to the public — with paintings by such masters as Rembrandt, Rubens, and Velázquez
▲▲ Natural History Museum A Darwinian's delight, packed with stuffed creatures, engaging exhibits, and enthralled kids.
▲▲ Greenwich Seafaring borough just east of the city center, with Cutty Sark tea clipper, Royal Observatory, other maritime sights, and a pleasant market.