The quickest option is the Southeastern train service which takes just 17 minutes from Charing Cross station and as little as eight minutes from London Bridge.
And best of all a Zone 1-2 Travelcard is valid for your journey.
The walk from the rail station into the town station takes less than five minutes and leads you past the pretty row of shops on Greenwich South Street, past the bottom of Royal Hill, where you will find an inviting row of village shops and pubs.
Cutty Sark for Maritime Greenwich, as Greenwich's most central DLR station is known, is a 23-minute direct journey from Bank tube station - catch any train heading to Lewisham.
Alternatively you can get the Jubilee line to Canary Wharf and change to DLR there.
There is another DLR stop at Greenwich railway station. Try and grab a seat at the front of the train as the views passing through Canary Wharf, as well as the glimpses of subterranean engineering, are great.
Until October of this year you also have the choice to alight at Island Gardens, where you have a splendid view of Greenwich, and walk through the famous Foot Tunnel which runs 50 feet under the Thames. For more information on DLR services visit www.dlr.co.uk or for help with planning your journey go to www.dlrlondon.co.uk/plan-your-journey
To Greenwich town centre: 129, 177, 180, 188, 199, 286, 386 The 188 bus from Russell Square comes through the town centre on its way to North Greenwich underground station and it serves 24 hours a day.
Greenwich town centre is also served by the 129 (from North Greenwich to Greenwich), the 177 (Thamesmead to Peckham), 180 (Belvedere to Lewisham), 199 (Canada Water to Catford), 286 (Greenwich to Sidcup via Eltham) and 386 (Blackheath Village to Woolwich).
The 53 (Oxford Circus to Plumstead) runs past the Blackheath Gate entrance to Greenwich Park, but does not go through the town itself. The night bus N1 goes from Tottenham Court Road to Thamesmead.
Perhaps the most relaxing way to travel to Greenwich is on the river - it's a regal way as you'll be taking the very same route as did Queen Elizabeth I in her day (albeit she was in a rowing boat).
Thames Clipper runs a frequent and reliable service, leaving every 20 minutes, and calling in at all or most piers along the way, providing plenty of opportunity to hop on.
Departure points, going east from the centre of town are Waterloo Pier, Embankment Pier, Blackfriars Pier, Bankside Pier, London Bridge Pier,Tower Pier, Canary Wharf Pier, Greenland Pier and Masthouse Terrace Pier.
If you're travelling on to the O2, stay on until the QEII pier (or get the express direct service if you're heading to a concert). The Clippers are all wheelchair and pram accessible at boarding points, in the interior and in the toilet facilities (yes, they have loos!).
There are bike racks outside Waterstone's on Greenwich Church Street, across the road from Café Rouge on Stockwell Street, outside St Mary's Gate to Greenwich Park and in the grounds of the Old Royal Naval College.
Greenwich is not only a lovely place to walk around, it's a lovely place to walk to. There are even organised walks to Greenwich with Metropolitan Walkers.
It has to be said that the roads around Greenwich town centre are very busy and so if you can travel by public transport that's the best and quickest option.
If you do travel by car there are off-street pay-and-display car parks in Park Row, Burney Street (behind the Ibis Hotel) and Park Row (to the east of the Old Royal Naval College, a three minute walk away from the town centre).
For information on where you can park your car, please click here.