The first thing you should do is to learn pronunciation of this interesting historical place. Greenwich is not "green-wich", as everyone tends to say. It is "gren-idge".
We start our walk from Greenwich railway station, which we can reach by train from London Bridge station in about ten minutes. We walk North-east from the station along the pavement (US: sidewalk) on the left. On the right we see a red building with a tower. This is the local library, which was opened in 1907. Going a little further, we see a square on the other side of the road, where there is a market on Saturdays and Sundays. Right next door is the Greenwich Picturehouse, a five-screen cinema with a bar and two restaurants. It was opened in 1989, but was completely rebuilt in 2005. Ahead is the French-style restaurant Café Rouge, come in if you're peckish... As you go on, the road bends slightly to the left, and you reach St Alphege Church. On the other side of the road is the flea market, which is open every day of the week except Monday.
At the next junction we turn right onto a street called Nelson Road. Of course, this street bears the name of the famous admiral, who died in the Battle of Trafalgar in 1805, but the troops led by him defeated Napoleon's troops. You must have already seen his statue right in the city centre...
At the next crossroad, we turn right again onto King William Walk. On the corner is the Nauticalia store, whose advertising slogan is: "First Shop in the World!" Indeed, this shop is located almost at the prime meridian, 00o 00.4'W. Soon we will see the Davenport House building on the left, in front of which is the peculiar sculpture Throne of Earthly Kings. I can't say what exactly it is, strange thing. Soon we reach the gates of the park. But we won't enter yet, we'll move to the left to see a few more things. In front of us is the statue of William IV (1765..1837). This statue once stood right in the city centre, but in 1935 it got stuck in front of the traffic and was "banished" here. On the right is a tiny water channel in a stone gutter, where dog owners cool their pets in hot weather. Soon we reach a building called the Sammy Ofer Wing NATIONAL MARITIME MUSEUM (the sponsor's name is in front!). The museum is free, but there may be paid exhibitions. Of course, there is also a cafe, but personally I would like to postpone the coffee - there is a better place ahead. ;-) In front of the building is a glass bottle several meters long, which of course contains a ship model. It originally stood on top of the famous "Fourth Plinth" in Trafalgar Square in 2010, but was brought here a few years later.
Soon we reach the gate and can finally enter the park (74 hectares in size). It is one of eight so-called royal parks in London. We move straight ahead until we reach a small staircase that forms a kind of stone stage. From there we go 45 degrees to the left up a steep hill. It is impossible to get lost, because this path is thickly full of tourists pushing up.
We reach the top of the hill. Here at the statue of General James Wolfe you have a great view of the city. Directly in front of us are white houses connected by galleries. This is the so-called Queen's House. Rebuilt over time, but essentially the house where the infamous King Henry VIII was born. Behind it, the skyscrapers of the financial centre Canary Wharf can be seen on the horizon. The four chimneys of the power station and the Millennium Dome, which we now know as the O2, can be seen on the right. The high-rises of the City can be seen on the left. But let's look at the other side. The famous observatory building stands there. Designed by Sir Christopher Wren. It cost £520 to build. Inflation has been strong in the meantime... There is an interesting clock in the 24-hour system on the wall, which was designed by Charles Shephard and has stood here since 1852. There is an iron fence in front and behind, and it costs quite a bit to get into the observatory (if you want to buy a ticket, £16, go through the doors into the building and turn right in the courtyard). Pay attention to the red orb at the top of one of the towers. It is at the top of the pole in the morning and falls to the bottom position every day at 1:00 PM. According to this, shipmen can set their watches on the river. However, you only need to buy a ticket if you want to see the entire observatory from the inside. There is a lot to see for free. For example, you can look at a 28-inch telescope for free if you know how to search. Go to the gift shop in the main building and find the stairs going up. There is a metal spiral staircase ahead and you are at the telescope. Totally free.
Let's move on. South of the observatory is The Pavillion Cafe, an interesting octagonal building. There you can eat and drink coffee. The cafe has a large terrace, where you can drink coffee in the fresh air and admire the surroundings.
Next, we could move on to the flower garden. While mainly tourists crowded the observatory, here the local residents rest in good weather. Entire families gather here to spend time lazing on the grass. I won't give you an exact route, see what you want. There is also a large body of water with waterfowl.
As we move on, a cherry alley will be on our way. Understandably, it is especially beautiful in spring. But to get an idea, google "greenwich cherry blossoms". You can see hundreds of pictures.
We move on to the rose garden. The roses are planted in the shape of semi-arches and there are really an awful lot of these. The garden was built in the sixties of the last century. On the western border of the garden is the Ranger's House. A park ranger once lived in it. The back side of the building faces the park, you can go to the front of the building from the small foot gate on the south side. This house now houses an art collection, which can also be explored for £9½. From April to October, at 11..17; from Sunday to Wednesday. But let's leave the south gate of the rose garden for a moment to admire the queen's bath. It's called Queen Caroline's Bath and it's a tiny pool. It is currently in a rather poor condition, it was probably in better condition when King George IV's wife used to bathe there (she lived in a nearby house called Montagu House, but it was demolished in 1815). Immediately to the right is a plaque on the wall commemorating a local resident named Ignatius Sancho. He was born in 1729 on a slave ship and later settled here. He is believed to have been the first black person ever to stand in a British election.
We are now on our way back north. On the way we see tennis courts on the right. Just before the descent from the hill begins, a particularly beautiful view of the "financial capital" Canary Wharf opens up between the trees. The tower of the church can be seen to the left of the same. There is a Catholic church with a particularly strange name: Our Ladye Star of the Sea. On the right side of the road, however, there is a strange shape that indirectly resembles a human figure. It's called Knife Edge.
If we turn left after leaving the park, we will soon reach the fan museum. It is located in two very peculiar houses. Maybe of interest? On the way back, we pass the Cutty Sark, which is currently ashore and contains a restaurant. It is a former tea clipper that transported tea from China. After all, the English are known tea lovers. The name means short shirt and comes from an old sailor's song about a witch. Right on the bank of the river is a small building with a dome, which is the entrance to the pedestrian tunnel. This tunnel was once built for the dock workers to get to their jobs on the other side of the river faster. You can go down 15 meters by stairs, but maybe you prefer the century-old lift. The northern end of the tunnel is narrower. This is a fixed place because during WWII the tunnel was hit by a bomb. Ice cream is sold at the exit on the other side of the river!
In addition, a couple of places marked with numbers on the map (if you are interested):
1. Queen Elizabeth's Oak (remains of an oak; a favourite place of Queen Elizabeth I, of course; it is also assumed that Henry VIII went there to dance with his wife Ann Boleyn, later "danced" Ann also with others and her head was chopped off)
2. Roman Temple (ruins, little remains)
3. Roman Motherstone Fountain
5. House with number zero (0 Circus Street)
6. Large indoor market