It’s got telescopes and periscopes. Canalettos and pedalos. Roaming deer, exploding stars, singed galleons, Nelson’s bloodstained knickers, about 106 museums, even more market stalls, and the best view in London. The Royal Borough of Greenwich is officially in charge of time, and appears hellbent on making sure not a second of it gets wasted.

It seems careless, in fact, to hide a place so action-packed in an insalubrious corner of southeast London, when it could be out in the shires, stealing a few visitors from Oxford or Bath. Londoners think of Greenwich as an afternoon out, nonLondoners barely think of it at all – yet shoehorned into this neat green rectangle of parkland beside the Thames are the Royal Observatory, the National Maritime Museum, the Old Royal Naval College and the Painted Hall, the most extravagant dining room in the western world. Not to mention the Cutty Sark – which we won’t, since it looks like a barbecued mackerel just now.

The park is glossy, the pubs are great, the shopping is quirky and the atmosphere is holiday-like. Going now would be especially good timing, as Greenwich prepares to toast its 10 years as a Unesco World Heritage Site with a month of street carnivals and open days (www.greenwichwhs.org.uk). Your perfect weekend itinerary starts here ...

DAY ONE
10.30am: whether you step off the river liner from Westminster (www.citycruises.com; £7.20) or emerge from Cutty Sark DLR station, Greenwich makes an instant impact. Christopher Wren’s double-domed palace, the best range of baroque buildings in Britain, lounges across the riverside lawns, with the silver towers of Canary Wharf rising bang opposite like rocket ships.

Except that this is not a palace, it’s an old folks’ home. The Old Royal Naval College began life as a hospice for scuttled 18th-century sailors, who spent most of the time dragging their wooden legs into unsavoury liaisons with local wenches. For the debauched details, you need to join the 11.30am tour with a yeoman guide (book on 020 8269 4791, www.oldroyalnavalcollege.org; £4), taking in historical highlights (“This is where Raleigh laid his cloak over a puddle ... that’s where Nelson’s corpse came ashore in a sherry barrel ...”), decent jokes and a go on the seamen’s underground skittle alley, where you get to bowl 150-year-old musket balls at antique belaying pins.

Don’t miss the Painted Hall – very like the Sistine Chapel, but a hospital canteen, created for the old salts to eat mutton and beans. And do have a sit-down in the colonnaded quadrangle of the Trinity College of Music, where tubas parp and pianos tinkle from every window, sending a discordant symphony out across the Thames. Weirdly enchanting.

1pm: if it’s Friday or Saturday, Greenwich’s flea market will now be jumping (www.greenwichmarket.net). To find it, follow the hum of Tibetan singing bowls along medieval Turnpin Lane. Here, stall space is evenly shared between vintage clothing (tulle skirts, granny dresses), chichi crafts (netsuke carving, “ethically sourced” silver) and beguiling tat (men with beards rooting through 1960s sci-fi annuals). It is top-drawer mooching territory.

Next, we’re off to the park, so consult the weather. If it’s sunny, head for George of Greenwich, on Nelson Road, to buy your deli picnic: Stinking Bishop cheese, San Daniele ham and stuffed olives, perhaps. If it’s damp, swing by Greenwich Church Street and buy a zany pair of wellies from the super-groovy shoe emporium Bullfrogs.

3pm: every day feels like a summer Sunday in Greenwich Park (www.royalparks.gov.uk). Its apron of greensward sweeps steeply down from the Royal Observatory to the river, with ample space for two kinds of afternoon: a child-friendly one of squirrel-chasing, pedal-boating and jumpers-for-goalposts kickabouts; or a grown-up ramble taking in Saxon barrows, medieval deer and modernist sculpture.

Either way, make sure that by sundown you’re on top of One Tree Hill, where Anne Boleyn played ring-a-roses with Henry VIII. From up here, you can scoop up the whole of London in a single, scintillating swivel – from the Millennium Dome to the more ancient dome of St Paul’s, via Canary Wharf, the Gherkin, the London Eye and Tower Bridge. And beyond, if you’re lucky, a biscuit-orange sun will be preparing to dunk itself into the Thames.

6pm: check in at the Devonport House Hotel (0870 609 1143, www.devere.co.uk; doubles from about £130), built as a nurses’ home for the naval hospital, now with shipshape bedrooms and military heroes sleeping soundly in the mausoleum on the grounds – see if you can find Thomas Masterman Hardy, famously snogged by Nelson on his deathbed.

Then it’s off round the corner for dinner at the Spread Eagle (020 8853 2333; two courses £27), Greenwich’s 18th-century coaching inn, where you can eat zesty French food while perusing the maritime art collection – so good, they hand out a catalogue with the menu.

DAY TWO
10am: today, we dive headfirst into Greenwich’s seafaring past, starting with a couple of hours at the National Maritime Museum (free; www.nmm.ac.uk).

It’s barely enough time: bigger than your average cruise liner, the museum’s central hall is a vast glass glacier mint full of pumping pistons, whirring propellers and winking lighthouses. So far, so macho. But for all the interactive stuff, it’s still the artefacts that really shake you up. No amount of push-button tsunamis could have the power of Nelson’s bloodstained breeches, cut from his body after Trafalgar; or the gnawed snow boots recovered from Sir John Franklin’s fatal Northwest Passage expedition, lost in the ice in 1847. The Victorian Establishment didn’t dare tell Franklin’s adoring public about the knife marks they found on the skeletons, evidence of cannibalism.

12.30pm: peckish? After a morning like that, lunch has to be a traditional whitebait platter at the Trafalgar Tavern (020 8858 2909; £7). This lived-in old boozer is Greenwich’s unofficial figurehead, teetering on a prow of land above the Thames. The pub was built 30 years after the battle, but at high tide, you could easily be amidships on HMS Victory: the tall Georgian windows are slap by the river, and the scrubbed floorboards seem to roll with the breaking waves – especially after a few pints of Trafalgar bitter.

2.30pm: one last journey to make. Wander back to the Maritime Museum and catch the 2.30pm shuttle bus to the beginning of time.

It trundles up to the top of the park, where the Royal Observatory (0870 781 5296, www.nmm.ac.uk; free) dominates the skyline – a Willy Wonkaish affair, with green onion domes and a red gobstopper on the roof, which is actually a giant pip, descending daily at 1pm as a time signal to passing ships.

Greenwich has been the world’s timekeeper since OldRoyal an international conference Naval fixed the line of zero longitude College here in 1884. Today, you can have your photo taken astride the prime meridian, or carry it around with you on a souvenir T-shirt. Inside the observatory, meanwhile, is a galaxy of exhibitions, from the intricate (John Harrison’s grapplings with the longitude conundrum) to the interplanetary (a new whizz-bang gallery where you can send a virtual space probe to Venus).

The really memorable bit, though, is the new Peter Harrison Planetarium (£6), where you tilt back in an armchair and watch stars detonate and universes collapse on the big screen above. Talk about finishing your weekend with a bang.

More information: Greenwich Tourism (0870 608 2000, www.greenwichwhs.org.uk).