Joint GLA/EDI base would be absolutely bloody awesome for me.
I would live in Stirling... good access to the highlands for your days off and about 45 minutes to both GLA and EDI.
No use if you're trying to do it on public transport though. For that I'd probably go for Cumbernauld (slightly easier for GLA) or Livingston (slightly easier for EDI).
BTW Hamilton's no use for anywhere. Too far south.