In extended canon (as in spec books and such), there are at least all these shipyards in addition to those mentioned above. They would all have repair capacity as well as construction and living quarters at a minimum. Some repairs take a very long time or require external life support so it comes as standard.
Assuming that we are talking about prior to the arrival of the Borg which would destroy a number of these. 40 Eridani A Starfleet Construction Yards, Acamar Prime Shipyard, Aldea Prime Shipyard, Altair Prime Shipyard, Andoria Prime Shipyard, Antares Ship Yards, Barcon Prime Shipyard , Barisa Prime Shipyard, Beta Antares Ship Yards, Bolarus Prime Shipyard, Calder Prime Shipyard, Centauri Spadeworks, Cestus Prime Shipyard, Copernicus Ship Yard, Deneva Shipyards, Denocet Prime Shipyard, Dytallix Prime Shipyard, Earth Station McKinley, Erabus Prime Shipyard, Finnea Prime Shipyard, Galor Prime Shipyard, Gavor Shipyards, Gibraltar Shipyards, Idran Prime Shipyard, Invernia Prime Shipyard, Iyaar Prime Shipyard, Janus Prime Shipyard, Ledonia Prime Shipyard, Meldrar Prime Shipyard, Merak Fleet Yards, Minos Prime Shipyard, Morena Fleet Yards, Moriya Prime Shipyard, Nausicaa Prime Shipyard, Oyarsa Prime Shipyard, Proxima Maintenance Yards, Qualor Prime Shipyard, Riverside Shipyard, Salazar Shipyard, San Francisco Fleet Yards, Tau Ceti Prime Shipyard, Taurus Prime Shipyard, Tellar Prime Shipyard, Tessen Prime Shipyard, Tranquility Base, Tri-Rho Nautical shipyards, Utopia Planitia Fleet Yards.
Now the manufacturing is out of the way, lets look at internal ship accommodation.
If we move to starbases with internal docking like Earth's one, you'll find that it's a 'cookie cutter' external design that is scaled up or down to fit needs (according to the Tech Manual) called the Spacedock-class. Designated classes will tell you what does what. Starbase 2 for example is a K-class with a general design that looks like this:
Note 3 arms coming from the centre. This is Starbase 343, but like all it bears K7 markings as DSS K7 was the first of it's design.
K-class still can dock cargo ships internally, but hasn't got the space for a ship like the Enterprise or even Akira class. It will happily take quite a few Sabres inside though, or 2 trade vessels. Part of the reason that trade ships were long and thin were to fit into K-Class and other smaller starbases.
Back to the Spacedock-class, there are only 5 built. Every other one is a military installation that flat-out OP's anything but a direct armada assault. 40 phaser banks huge result capacity and ability to hide a large fleet etc etc. Earth one doesn't have guns because politics but you already know that.
Finally, it was said earlier that the space dock at earth was grown in size for video after new bigger ships arrived... well officially, the doors are resized on all Spacedock-class bases whenever a larger warship is made. For a long time these were the only non-shipyard facilities that could internally dock warships.
Anyway, the full list is as follows:
Lya Station Alpha
As for other classes a few come to mind:
The Sigma/R1 class starbase would have docking facilities for cargo ships internally. You don't actually see any of these until the 24th century and are refitted to Sigma class, but the R1 class of the 23rd was visually the same allegedly.
Note that the Nor class has 3 'stalks' and the Frontier has 4.
DS9 is a Nor-Class Starbase which had many clones too, as it was originally called the Terok Nor under Cardassian possession. There is also the Elvok Nor and Empok Nor which are almost visually identical. It's replacement was a Fed Frontier-Class staircase which again is one of the only other large military installations the Fed have possessed.