Greenwich was once a village separate from London, now swallowed by the sprawl, but it's managed to retain the feeling of a 17th century fishing village and centre of Britain's Maritime glory - just. The Observatory sits on the hill in the park, marking East from West at its meridian, and the Queen's house and Naval College look down towards the historic waterfront with the well preserved 19th C tea clipper 'The Cutty Sark'. The maritime museum is great for kids and adults alike and the weekend market is worth exploring, as is the nearby Georgian village of Blackheath (a poor cousin to Hampstead) for its architecture.
The best way to approach Greenwich is via the creepy Victorian foot tunnel under the river from Island Garden's DLR station (catch the DLR from the Tower of London). In summer it's pleasant to travel to Greenwich as Pepys did in 1665: by boat - you can pick up a cruiser to Greenwich from Westminster Pier by the Houses of Parliament or from the Tower. Otherwise the train from Charing Cross or Waterloo East Stations is fast and frequent. The sad thing about Greenwich is the almost total absence of good restaurants.