Surely the most important aspect is whether the building is suitable for today's (and future) use as an archive?
No, I disagree with you. Quite strongly.
The most important thing is preserving convenient access for users. Putting the whole thing in a seedy peripheral industrial estate with a shortage of parking* and poor public transport* would be catastrophic. If people cannot easily get there, they won't go, and if they don't go the demand for the service will fall and that will provide the Powers That Be with a pretext for reducing it still further.
(*How are the staff going to get to work when the nearest bus stop is 10 minutes' walk away, and there's no parking?)
That could mean further reductions in opening times (or ultimately complete closure).
It could mean that archive material is dispersed or even destroyed. Remember djct in an earlier thread here telling us how (s)he was involved in the destruction of various records which no-one throught would be useful, but which would now have been extremely useful and much sought after?
There must be ways of economising that would still maintain city centre access to the material which is most in demand. I understand that it isn't possible to keep everything in the same place, but I don't think that moving lock, stock and barrel to Sighthill, let alone building a new Records centre somewhere out in the sticks, is the answer.