Faslane, the SNP have said many times, nope, no way.
Legally it doesn't matter. Scotland has no constitutional right to unilaterally leave the UK. It's the same for Cornwall or Aberystwyth. Scotland's status as a "country" within the United Kingdom doesn't change anything. As such, if the SNP don't like the terms offered it, the UK government can stop Scotland from leaving.
It wouldn't be the ideal way forwards, but it would be leverage to get the best deal for the UK. Otherwise what will happen is the SNP will try to skip out on its share of the national debt, because that would be much more valuable than any small share of assets available. There's also the issue of where the dividing line will be for fisheries and oil/gas. Even the status of military personnel would be something difficult. The SNP would be concerned about the UK poaching "their" military professionals, but the British military doesn't have the spare capacity to not absolutely be offering everyone already in the Armed Forces to stay on rather than join a Scottish Army et al. Again, that's not something the SNP can be allowed to have a veto on.
At some point hardball will have to be played by London - Faslane would probably not be the biggest sticking issue.
The cost of relocating would be hideously unaffordable.
That could be priced into a phased withdrawal from Scotland from the UK - Barnet costs the rest of the UK as much as £15 billion a year just for Scotland. If Scotland was allowed time to break away to get its house in order, that could be reduced or axed beforehand as a price of not having Faslane stay open for the SSBNs. That stacks up very quickly into a fat budget for a new naval facility.
The screaming about the deterrent not being indepedent goes on to this day
Indeed. However, politicians are politicians, and when under pressure they can be pushed in ways they'd prefer they're not.
Coming at this from the political angle, Kings Bay
might work for the long-term, but it would probably require a treaty with the US and Congress passing it into law to ensure a future President (e.g. Trump 2.0) didn't demand silly money for "rent".
France is a no-go politically. Even when an "Anglophile" French President comes along, they inevitably turn on us at least once when they're put under domestic pressure by fishermen, unions or the Gironde-Sud Mamans Alliance. I'm struggling to think of the legal and constitutional safeguards that would be sufficient.
And in any event, if there's a kerfuffle about shifting the deterrent to a foreign country, leaving it in a newly independent Scotland doesn't resolve that tension.
If SSBNs were to stay in Scotland, I expect there would be a legally-watertight lease (possibly renewing) built into the withdrawal agreement. That would have a higher legal standing than a treaty agreed with the US or France, because it would be part of the terms of which Scotland left the UK.