I got really lucky with a weather because when I left a house sky was perfectly and evenly gray but by the time I reached Greenwich it was nice and sunny :)
I started from Cutty Sark (a ship), then I headed to Greenwich Market. Usually I like to by something to for lunch at the market and go to Greenwich Park, sit on the grass and have a mini picnic. Park is pretty big and is very beautiful. You can lots of flowers, there's a rose garden which wasn't blooming yet, a place where you can go watch deer (unlike Richmond park they are not roaming free), visit Royal Observatory and see Meridian line, enjoy beautiful London views.
Just right next to the park there's National Maritime Museum which should be very nice place to visit but I haven't been inside yet.
Very close to the park there's also very small but lovely Fan Museum. They have 3 exhibitions a year and it's very interesting to see all these small pieces of art.
And between the park and the station there's Old Royal Naval College which you would definitely recognize if you've seen any photos from Greenwich.
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