I believe the only bases you CANNOT repair at are the Pleasure Planets, as they are teh only ones without ship dealers, although refineries may fall into this as well, it has been a dozen years since I really played WC:P

Pleasure Planets never have ship dealers. Some other bases do not have them as well but the vast majority of planets/bases do.

I must have terrible luck then. I just found a 2nd repair base in the Junction System. I've been to at least 10 different bases across all quads before(mining/farming/pleasure) and none of them had a repairs available.

All 3 in Troy have repairs.

Contrary to previous statements, Magdaline has a ship dealer even though it's a pleasure base. I am noticing a lot of bases have dealers. It looks like I just had awful luck.

In theory all planets with a ship dealer can fix your ship.
You might also want to invest in a Repair Droid: those things can fix every damaged system on-board except for external components, like hull armor and weapons. It costs 35000c, but it is worth it.

yea, I was not sure what I'd go for next. I went straight for better guns right off the bat, so I got 2 particle cannons and 2 missile launchers. Then I decided to go for better armour and the best targeting system.

Roughly half of all bases in the game have a ship dealer (and can therefore repeair internal and external damage as well as restock missile or torpedo launchers). All four of the basic base types (mining, agricultural, refinery, pleasure) can have as many amenities as e.g. Achilles or just the bare minimum (mission computer, commodities exchange, bar). The four unique bases all have everything. It's uncommon for a system to have more than one ship dealer (Troy is definitely the exception here, as it's meant to be a "safe" place to start out), but nearly every system with one or more bases has a ship dealer on one of them.