Not to miss

Royal Observatory

In 1675 Charles II had the Royal Observatory built on a hill in the middle of the Greenwich Park, intending that astronomy be used to establish longitude at sea. The Octagon Room, designed by Wren, and the nearby Sextant Room are where John Flamsteed (1646-1719), the first astronomer royal, made his observations and calculations.

The globe is divided between east and west at the Royal Observatory, and in the Meridian Courtyard you can place one foot either side of the meridian line and straddle the two hemispheres.

Every day at 13:00 the red time ball at the top of the Royal Observatory continues to drop as has done since 1833. You can still get great views of Greenwich and spy on your fellow tourists at the same time by visiting the unique Camera Obscura. An ambitious 15 million project has added four new galleries exploring astronomy and time, including one on the search for longitude.

The 120-seat state-of-the-art Peter Harrison Planetarium (tel: 8312 8565; hourly shows 13:00-16:00 Mon-Fri, 11:00-16:00 Sat & Sun), which opened just south of the Royal Observatory in June 2007, has an around 1 million digital laser projector that can show entire heavens on the inside of its bronze-clad roof and is the most advanced in Europe. Along with the theme shows, there are galleries tracing the history of astronomy and interactive displays on such subjects the effects of gravity.

London Eye

It takes a gracefully slow 30 minutes and, weather permitting, you can see 25 miles in every direction from the top of the world's tallest Ferris wheel. To the west lies Windsor, while to the east the sea. In between, you have the chance to pick out familiar landmarks. A ride in one of the wheel's 32 glass-enclosed gondolas holding up to 25 people is something you really can't miss if you want to say you've 'done' London.

It's difficult to remember what London looked like before the landmark London Eye began twirling at the southwestern end of Jubilee Gardens during the millennium year. Not only has it fundamentally altered the skyline of the South Bank but, standing 135m tall in a fairly flat city, it is visible from many surprising parts of the city (eg Kennington and Mayfair).

You can save 10% on standard 'flight' - as sponsor BA likes to call it - prices and avoid the queues to buy tickets by booking online (minimum two hours before your chosen time). Be sure to arrive 30 minutes in advance.

Tate Modern

The public's love affair with this phenomenally successful modern art gallery shows no sign of waning. Serious art critics have occasionally swiped at its populism (eg Carl Höller's funfair-like slides, Olafur Eliasson's participatory The Weather Project, both in the vast Turbine Hall) and poked holes in its collection. But 5 million visitors make it the world's most popular contemporary art gallery, and London's most visited sight.

The critics are right in one sense, though: this 'Tate Modern effect' is really more about the building and its location than about the mostly 20th-century art inside. Leading Swiss architects Herzog & de Meuron won the Pritzker, architecture's most prestigious prize, for their transformation of the empty Bankside Power Station, which was built between 1947 and 1963 and decommissioned 23 years later. Leaving the building's single central chimney, adding a two-storey glass box onto the roof and using the vast Turbine Hall as a dramatic entrance space were three strokes of genius. Then, of course, there are the wonderful views of the Thames and St Paul's, particularly from the restaurant-bar on the 7th level and coffee bar on the 4th. There's also a café on the 2nd level, plus places to relax overlooking the Turbine Hall. An 11-storey glass tower extension to the southwest corner in the form of a ziggurat - a spiralling stepped pyramid - by the same architects is now under way and will be completed in 2012.

Tate Modern's permanent collection on levels 3 and 5 is now arranged by both theme and chronology. States of Flux is devoted to early-20th-century avant-garde movements, including cubism and futurism. Poetry and Dream examines surrealism through various themes and techniques. Material Gestures features European and American painting and sculpture of the 1940s and '50s. Idea and Object looks at minimalism and conceptual art from the 1960s onward.

More than 60,000 works are on constant rotation here, and the curators have at their disposal paintings by Georges Braque, Henri Matisse, Piet Mondrian and Andy Warhol, as well as pieces by Joseph Beuys, Marcel Duchamp, Damien Hirst, Rebecca Horn, Claes Oldenburg and Auguste Rodin. Mark Rothko's famous Seagram murals have been given their own space on level 3; other familiar favourites include Roy Lichtenstein's Whaam! (level 5), Jackson Pollock's Summertime: No 9A (level 3) and Andy Warhol's Marilyn Diptych (level 5)

Special exhibitions (level 4) in the past have included retrospectives on Edward Hopper, Frida Kahlo, August Strindberg, Nazism and 'Degenerate' Art and local 'bad boys' Gilbert & George. Audioguides, with four different tours, are available for around 2. Free guided highlights tours depart at 11:00, noon, 14:00 and 15:00 daily.

The Tate Boat, painted by Damien Hirst, operates between the Bankside Pier at Tate Modern and the Millbank Pier at sister-museum Tate Britain, stopping en route at the London Eye. Services from Tate Modern depart from 10:00 to 16:40 daily, at 40-minute intervals .