Favourite Things to Do in Greenwich, London
I've lived in this area for over 15 years and spend the majority of my time in Greenwich. A lot of my errands are spread out in this vicinity (Greenwich, Deptford, Blackheath, Lewisham and Canary Wharf). One does not want to go into Central London unless absolutely necessary as it can be draining and you want to leave it for the fun occasions.
Greenwich is quite touristy at times but if you go in the middle of the week its a lot better. Generally the winter isnt as hectic either.
My favourite things to do in Greenwich:
Greenwich Picturehouse: I love the cinema and this is a chain of indie cinemas across the UK. The seats are a lot nicer than some other places, the food is better and its just generally quieter in my opinion. The memberships are quite a good deal as you get discounts and free tickets which generally pay for the cost of the yearly membership. The Galley Cafe right next door is the best place in Greenwich for a pot of chamomile tea and cakes. Its cheaper than Peyton and Byrne and if you can get there early you can avoid some of the mums with push chairs (this is not a bad thing but if you want to read can be crazy!)
Greenwich Market: This is always great fun to walk through especially around Christmastime. They do several antique/vintage market days and mostly its a strict handmade stall rule. You can find a lot of artisans selling their wares and unique gifts. Some of my favourite regular stalls/shops (I dont know their proper biz names) are the vintage camera stall who has proper film cameras of all sorts, I love the Ethiopian food stall (go for the meal deal that includes the samosas), the vintage clothes shop near the middle is always fun to look around and the health food shop (Greenlands I think is the name) is always great. If you want something to eat get something from the market as its the cheapest and best option!
The Queens House (pictured above): They've recently re-done this beauty and its a wonderful chance to walk around and look at some art and history. The spiral tulip staircase is stunning and probably the most Instagrammed thing you'll see in Greenwich. Its a lot quieter than the National Maritime Museum which can be over-run with annoying kids (although its good to keep an eye out for exhibitions--they've had some good ones in past like Ansel Adams, etc).
Greenwich Park: This place is my oasis. Its big enough you can have a few minutes to yourself and not know you're in London. The spring time/early summer is my favourite. Up on the very top near the gate for blackheath there's an entire row of Cherry Blossoms that you can see that will just take your breath away. There's also the Meridian Line (it costs to go in), the Royal Observatory and the secret garden where you can see an entire herd of deer. Its perfect to run around and often many weekends you'll see running races here. The most quietest places in the park are further up the hill as people tend to gravitate towards the entrances (the hill can be tricky!)
Wandering Round Old Royal Naval College/Cutty Sark: This is one of the more historical parts of Greenwich and is used frequently for the backdrops for film/TV shoots. The list is long including Pirates of the Caribbean, Les Mis, the Kings Speech and the Crown. You can wander inside the Painted Hall which is incredible and then walk down towards the Thames. In the summer its quite nice to wander round the Thames path as there's cute little pubs and photogenic little corners. The Cutty Sark is fun too but not one of my more favourites--probably because I've been around it so much. Its worth a look if you have time and you can get a good photo from underneath the boat. Speaking of boats---one really fun thing to do is catch the boat from Central London and take it back to Greenwich. Its a lot more restful way to get home than fighting your way on the underground!
Best Pub: Greenwich Union--If you want a traditional pub food experience without getting sick this is the place. Its a bit quieter than the food places in the centre and its a lot of food, good quality and good price. Its near Greenwich train station and if you want to wander round this part of Greenwich its the best for an Instagram photowalk. The Creaky Shed is a cute place and you can always find some good classic cars along the side streets.
If you need other ideas for decent places to eat besides the market and this pub: Marks and Spencers Food has good take away stuff if you want to eat in the park, Heaps Sausages, Goddards Pie Shop and Honest Burgers.
Greenwich is a place that a lot of people dont get to sometimes when they come to the UK but its worth it if you have the time!