Not to miss

Royal Observatory

Standing with one foot in the world's western hemisphere and the other in the east: that's the Royal Observatory's cheap thrill. But as well as the chance to straddle the prime meridian (of time and longitude) there's also an absorbing tale of how the observatory's astronomers battled to accurately measure longitude, and help improve maritime navigation.

Charles II, sick of ships foundering because they had no idea of their east-west coordinates, had the Royal Observatory built on the hill here in 1675, intending that astronomy be used to find an accurate means of navigation at sea. The first astronomer royal, John Flamsteed (1646-1719), set up home here, making observations of the skies and stars from the Octagon Room - a light, airy, geometrically shaped observatory that is one of the few interiors designed by Sir Christopher Wren to have survived.

Astronomy was a dog's life in those days, as the tales from the excellent observatory make clear. Today, however, that doesn't seem the case. At least, the astronomers who talk you through shows at the adjacent Greenwich Planetarium brim with enthusiasm. At night, look out for the green laser that traces the prime meridian in the sky.

In the end, it was a watchmaker who solved the problem of longitude, but Greenwich was still named as the prime meridian at an 1884 Washington conference, in recognition of all its work.

British Airways London Eye

The colossal London Eye (aka the Millennium Wheel). At 135m (443ft) tall, it's the world's largest Ferris Wheel and London's fourth-tallest structure. It's a thrilling experience to sit in one of the 32 enclosed glass gondolas, enjoying views of some 40km (25mi) on clear days across the capital.

The Eye is at the southwestern corner of Jubilee Gardens, site of the 1951 Festival of Britain, which now extends northwards to Hungerford Bridge. The Millennium Wheel takes a full 30 minutes to rotate completely and each capsule holds 25 passengers.

Tate Modern

A spectacularly converted power station, the world's most successful contemporary art gallery hasn't ever really been about the art, but about the building, location and views. So the recent rearrangement of its works into a more thematic and chronological order is a refreshing bonus rather than a vital reinvention.

The Tate's reputation for avant-garde special exhibitions is exemplified by past exhibits such as those focusing on the Italian Arte Povera (Poor Art) school and the sculptures of the late Juan Muñoz.

The building itself still continues to wow. With its two upper floors shrouded in glass and brightly lit at night, and its landmark central chimney, it was designed by Swiss stars Herzog & De Meuron (1999), who won the Pritzker award, architecture's Nobel Prize, in 2000.