Big yard, for me, means anything over size 50 or so. Bremerton is the biggest on-map yard. It's rated at 200 which means it can handle 200,000 tonnes of shipping. SF is 140, Mare Island and LA are both 90 and Portland is 70. There several others on the west coast between 50 and 3.
Of the non west coast but on-map ship yards the three biggest are Pearl (100), Colombo (40), and Sydney (30). Major damage repair can only be carried out at bases of thirty or above.
The biggest base of all is the Eastern USA, which is rated at 300. The UK is 100 with Capetown close behind on 80.
I would prefer to keep all the battleships at Pearl for repair but the 8 of them would far exceed the 100,000 tonnes limit and slow down work considerably so I have no choice than to move them on once flotation damage is under control. Bremerton, SF and Mare Island will receive most of them, I expect. The most badly damaged will remain at Pearl for a long time yet but I would rather have her clear for the future.
To be honest I hadn't realized Pearl had as large a Yard as she does. I thought it was about 50 or so. Still, all that space is getting used up quick.
By the way,
Repulse will go into the yard at Sydney, I think. Should be enough to handle her. Mind you, I think the smaller a base is the longer it takes, and I believe naval support squads are also a factor. But then, I have to factor in transit time to Pearl or Capetown and the extra risk involved plus expenditure of escorts, extra rum rations.....No, Sydney it is.