I've only seen the TV series, but it seems that even though Night's Watch has got multiple castles situated on and near the wall and there might be patrols going between them on the wall, Castle Black is the only Night's Watch's location that is shown there. Did I miss any coverage of other Night's Watch's fortifications? Is there any action happening in the books?
There were originally 19 castles or fortifications on the wall1, however as numbers waned the Night's Watch became fewer and fewer. This left just Three Castles manned. Castle Black, which you mentioned is located towards the centre of the wall and is effectively Night's Watch HQ. The other two are Eastwatch-by-the-Sea and The Shadow Tower.
Let's start with the easier of the two.
The Shadow Tower
Game of Thrones
The Shadow Tower got only few mentions in the series. It first made an appearance when Qhorin Halfhand and some other Rangers joined Jon Snow in scouting out the Wildling Army. Qhorin, Stonesnake, Borba and Harker all died in that scouting after Jon was taken.
It's second appearance was after the death of the Old Bear, when the Commander of The Shadow Tower, Denys Mallister came to the elections of the new Lord Commander of the Night's Watch. Although he was experienced, he ended up losing to Jon Snow.
A Song of Ice and Fire
Qhorin Halfhand leads a ranging from the Shadow Tower in A Game of Thrones, he is however unsuccessful in finding Benjen Stark, First Ranger of the Night's Watch. In the book series, Jeor Mormont considers repopulating Stonedoor with men from the Shadow Tower. Another difference is that the Rangers with Qhorin during the scouting that die are Ebben, Dalbridge and Stonesnake. The men from the Shadow Tower travelling to Castle Black pick up Sam and Gilly en-route, taking them to Castle Black. Regular raids are also discussed at the Shadow Tower.
Game of Thrones
Eastwatch made a bigger appearance in Season 7, after the Fellowship of the Wights met there to make there ranging into the North. This is where Jon and co. met before they went North to capture a wight and bring it South. It was also the castle destroyed by the Night King. In Season 7 Tormund and his wildlings manned Eastwatch.
It had minor mentions before Season 7, such as Tywin send Janos Slynt there, and Stannis advising Jon to send Alliser Thorne there, Jon however ends up deciding he wants to keep Alliser close.
A Song of Ice and Fire
Like at the Shadow Tower, Jeor Mormont considers repopulating Long Barrow with men from Eastwatch, Alliser Thorne is also made Master-at-arms at Eastwatch. Stannis lands at Eastwatch to save Castle Black, and Sam and Gilly set off from Eastwatch with Maester Aemon.
Cotter Pyke takes 11 ships to save the people at Hardhome on a rescue mission. The Giants trying to cross the wall with their mammoths are also sent East to round the wall at Eastwatch as the mammoths are too large to cross the wall.
So although they're very minor, they did have mentions.
1 From West to East they are as follows.
- The Shadow Tower, commanded by Ser Denys Mallister
- Sentinel Stand
- Greyguard (mentioned in show)
- Hoarfrost Hill
- The Nightfort (mentioned in show)
- Deep Lake (mentioned in show)
- Castle Black, commanded by the Lord Commander of the Night's Watch
- Sable Hall
- Long Barrow
- The Torches
- Eastwatch-by-the-Sea (Up until S7. gg Eastwatch)
There are numerous "castles" along The Wall. The show only seems to show two of these, though I believe other's may be mentioned:
There are other castles along The Wall, I believe these are the ones mentioned in the show:
- The Shadow Tower
- Deep Lake
Note that The Wall is long, around 300 miles, so patrols between the castles is unlikely. As The Wall is so tall and the only ways through are at the castles only the immediate area surrounding them appears to be guarded. This is further reinforced by that the Nights Watch are short on men and only appear to occupy Castle Black, Eastwatch and The Shadow Tower.
The following map also shows the rest of the Castles along The Wall:
Note that as of Seaosn 7 episode 7 Eastwatch appears to have been destroyed:
Source: Game of Thrones wikia
In the books, the only castles that are manned are Eastwatch, Castle Black and the Shadow Tower. The other sixteen are deserted and sealed up. I believe that there were never more than seventeen of the nineteen castles in use at any one time. There are occasional patrols by rangers and builders along the wall above the abandoned castles to check its condition and look for signs of wildlings.