With up-to-the-minute modernity layered on top of 2,000 years of history, it could take a lifetime to fully explore London, vibrant capital of both England and the United Kingdom. If your time is limited, here are five not-to-be-missed experiences.

Trafalgar Square is one of the world's most dramatic public spaces. Here at London's very heart, Nelson's column towers over a swirl of people and fountains, hosting public celebrations and protests of all kinds. In the rain, the square glistens with reflected light as Big Ben glows in the distance down Whitehall.

A great time to visit Trafalgar Square is Thursday or Friday evening when the National Portrait Gallery (to the side of the National Gallery) is open late. After marveling at portraits of Tudor wives and modern pop stars, nip across the street into the futuristic elevator that descends to the crypt of St-Martin-in-the-Fields church. Make a brass rubbing, then dine on fresh fare in the Cafe as candlelight flickers on the crypt's vaulted ceiling. It's a popular spot that bustles when classical concerts are scheduled.

The English are great gardeners and Hyde Park is London's green masterpiece. If you want to dodge the museum crowds, grab a bag of scotch eggs and salad from Marks & Spencer and hike from Buckingham Palace (just east of Hyde Park Corner) to Kensington Palace (at the park's west end), stopping to soak up quintessential English scenes: girls on horseback trotting down Rotten Row, daffodils blooming around the Peter Pan statue in Kensington Gardens, children floating boats on the Serpentine. A cafe overlooks the water but why not end your idyllic afternoon with high tea at the Dorchester Hotel on nearby Park Lane? Be forewarned, reservations for high tea can be booked up to a month in advance.

Five hundred years of theatrical tradition has made London the world's premier theater destination, with so many venues concentrated in the West End that it has been dubbed Theatreland. Everyone attends and you'll find the latest reviews on everyone's lips, including your cabby's.

There is a lot on offer, from splashy musicals to dramas featuring A-list film stars taking a breather from movies to maintain their stage cred. You may be surprised to find out who's appearing during your stay. Theatergoing is such an essential part of any London experience that you should check theater listings before booking your flight. You wouldn't want to miss your favorite actor by a week or two!

Seats can be booked online ahead of time or stop by any theater at the last minute and grab what's available. If you arrive early and are feeling bold, hover around the stage door and try to snag an autograph. Many theaters are a century old or more and cocktails at intermission add to the ambiance and fun.

Atmosphere, atmosphere, atmosphere ... from Traitor's Gate to the Bloody Tower, this UNESCO World Heritage Site has it in spades. Established by William the Conqueror nearly 1,000 years ago and serving as a royal residence right up to James I, the Tower's romantic reputation rests largely on its role as prison and place of execution for, among others, Henry VIII's ill-fated wives Anne Boleyn and Catherine Howard. Photogenic Beefeaters, scary armor, the Crown Jewels and one of the best gift shops in town make the Tower a must-see for all ages.

Zip past the ticket lines with a London Pass. Then, after you've walked and climbed your feet off, why not leave by boat? Cruising the mighty Thames down to the Palace of Westminster (and the nearby Abbey) is the easiest way to spot and photograph other London icons such as Tower Bridge and the dome of St. Paul's Cathedral.

Europe's largest observation wheel looms elegantly on the south bank of the river, just north of Westminster Bridge. Climb aboard this engineering marvel and rise 443 feet above the city in a glass pod that affords 360-degree views for 25 miles in all directions. Though the guidebooks recommend buying timed tickets in advance, it's best to make a "day of" judgment call as visibility depends on the weather. Splurge on a Fast Track ticket to jump the queue and save valuable touring time.

The "flight" is more thrilling than frightening. The wheel moves at an almost-imperceptible speed but never actually stops so you must step into, and out of, your pod while it creeps by. Don't worry, there are staff standing by to assist. On a clear day you can see 14 counties and spy all those sights you couldn't get to on foot. At night, it's absolute magic.

Photo credits: Trafalgar Square, London Eye - Michele Peterson; Hyde Park, Tower of London, Theatreland - Lesley Peterson.