Map of London Greenwich tube station
Greenwich is famous for four things, though three of them are intimately related: Greenwich Mean Time (GMT), the Greenwich Meridian, The Royal Greenwich Observatory, and the Royal Naval College.
You can discover all about the first two by visting the the Royal Greenwich Observatory, up on the hill above the Naval College. Although observations no longer take place here (the active observatory has long since departed), the place is a fascinating museum of astronomy and the history of measuring time. Here you can stand with one foot in the Eastern Hemisphere and the other in the Western Hemisphere. (of course you can do this elsewhere too, but here it seems most significant!)
There is a foot tunnel under the Thames, but which you can walk to the Isle of Dogs and Island Gardens DLR station (but check first to ensure that the trains are running). From here you can take the light railway to Canary Wharf, Tower Gateway or Stratford.
You can click and drag the map around to find nearby restaurants, attractions and pubs nearby:
Aldwych | Baker Street | Bank | Barbican Center | Bloomsbury | Camden Twon | Canary Wharf | Chancery Lane | Charing Cross Road | Covent Garden | Downing Street | Elephant & Castle | Embankment | Euston | Farringdon | Fenchurch Street | Fleet Street | Green Park | Greenwich | Hampstead | Hyde Park | Islington | Kentish Town | King Cross | Knightbridge | Leicester Square | Liverpool Street | Marble Arch | Marylebone | Monument | Oxford Street | Paddington | Pimlico | Regents Park | Sloane Square | South Bank | St James Park | St Pancras | St Pauls | Tower Bridge | Trafalgar Square | Vauxhall | Victoria | Wapping | Waterloo | Westminster | Whitehall | Woolwich