Sorry, don't know much about Falkirk or Stirling really apart from I like the castle and views from it.
Shawlands Academy or Hillhead primary and High are very ethnically diverse. Both secondary's though perform poorly on league tables.
I think the problem with Glasgow schools are the league table results. I know not everybody holds alot of store by these but it was enough to put me off wanting my children to attend a secondary in Glasgow. Though I went to school in Glasgow and did ok but alot of my friends didn't.
Though you will probably find that even if you can't afford to live in East Renfrewshire or East Dunbartonshire you could still get your children into these schools. If there is a space in the years your children are looking to enter then they have to let your child into that school. If your eldest would be in p4 then the school of your choice has to let your child into it if there is a space.
There are nice areas of Glasgow to live that don't necessarily have great secondary's in it. Some of my friends live in knightswood/yoker in Glasgow. Their children went to local schools for p1 then as soon as spaces came up in a school in Bearsden, they moved their child into it. Bearsden is East Dunbartonshire and quite close to knightswood/yoker.
The problem also is that alot of secondary's cover some very affluent areas but also some very poor areas. There is huge disparity in Glasgow between the affluent areas and the deprived areas. I think this vast difference drastically affects the schools.
Don't think this makes much sense but don't have time to correct as kids hungry again so need to go.