Many visitors to London don't realize how easy and cheap it is to get to Greenwich. Maybe some don't even know that Greenwich is so close to London. I'm here to tell you that if you’ve got yourself to London, you can get yourself to Greenwich and have a fabulous time doing it.
I've always found that one of my favorite ways to see a city is by public transportation (not counting tourist buses and the like), and the trip out to Greenwich has to be my favorite proof of that. In fact, there are actually two special routes there, and I still can't decide which I like more.
First of all, there's the new and very modern Docklands Light Railway. The fine print can be confusing, but the "DLR" is included in a standard Travelcard, which includes access to the Tube and busses. The DLR is not technically part of the Tube system, although it appears on the Tube maps and connects through the same Tube stations. Once you board a DLR, you'll see why this new system is unique. The most convenient place to grab the DLR is probably Bank station. Boarding here will definitely give you the most enjoyable ride. Make sure you board a train bound for Lewisham, since the rail lines split in two directions. Try to get into the front car, especially the very front seats, where you'll have a view from the front windows (the DLR uses a driver-less system, although the conductor will be around).
The first moments of the trip from Bank feel like the start of a thrill ride as you quickly accelerate through a dark tunnel. Suddenly, a light appears and you are thrust out into daylight out of the cramped city center and approaching the Docklands, an area outside of the city that is under much recent development. Because of the building codes in the city - until recently, no new construction could be higher than St. Paul's Cathedral - the tallest buildings in London are here, Canary Wharf. The elevated track actually takes you right next to these skyscrapers, twisting through the maze of buildings, again giving the impression of a theme park ride. The train goes underground again to cross the Thames, then drops you at Cutty Sark station (closer to most of the attractions than the next stop, the one actually named Greenwich) just a few steps from markets, pubs, parks, and museums.
On the other hand, it would be a shame to miss out on Canary Wharf Tube stop, another point of accessibility to Greenwich. On the Jubilee line, it may be closer than the DLR from your starting point. You get off here to catch the DLR over a few stops to Greenwich, again Cutty Sark station, but you actually have to go above ground to transfer, which turns out to be an okay experience. Canary Wharf is without a doubt the most beautiful subway or metro station I've ever seen. The long escalators to the street, which in this case is a plaza, are perched underneath a huge glass ceiling that drapes the whole station in sunlight. When you reach the top, you walk out in the midst of skyscrapers, but not in a crowded, bustling area. This is a business district that is practically abandoned during midday hours. Take at least a minute to take in a bit of Canary Wharf, an area gaining power and presence even separately from London, before you hop on the DLR to Greenwich.