Where to start....
There are cheaper commuter spots that are close to Edinburgh, like Falkirk for example. But I lived there for a while and found it too insular.
If you're used to travelling then I think somewhere with a hint of the cosmopolitan about it might help you to fit in/find like minded people.
Do you know what your budget is likely to be?
East Kilbride is a pretty reasonable place depending on area. If you see a house you like the look of I can give you an insight into the demographics of the area and it's amenities. East Kilbride is about 7 miles from Glasgow City Centre and is served by train and bus routes. It's very suburban but it has lovely country parks and woodland as well as a shopping centre and various sports grounds. The schools in East Kilbride are mostly fine. They're neither at the bottom nor right at the top.
Hamilton is cheaper than East Kilbride, arguably not as well serviced for public transport, but is similar demographically. It also has country parks, shopping precinct etc. However I feel the difference between the local schools is quite tangible. Particularly at High School.
If you move to a different council area: East Renfrewshire- you have the best performing schools in Scotland and a 5-8 mile commute to Glasgow. It's served by train and bus and has a more affluent demographic. Houses there tend to be more expensive than East Kilbride for example- but there are areas which are more pocket friendly. Parts of Busby or Stamperland for example.
The Southside of Glasgow is also an 'up and coming' area. (Historically the West End is the affluent, cultured side with good schools but it is £££££ and you'll never find a house there for an East Kilbride budget.) Shawlands and Pollockshields are closer to Glasgow- maybe only 2 or 3 miles and again, well served by bus or train. It's quite a buzzy area, feels slightly more urban than the areas further away from Glasgow. The schools are very multi-cultural, had some issues in the past but are improving year on year with good results.
Bishopbriggs is also a popular area with young families, it's in West Dunbartonshire. Pretty good schools. Mix of housing. Transport links are fine- there is trains and buses (perhaps not as well served as other areas in my honest opinion) but definitely easily commutable by car.
The school league tables for each area are available by different council websites as well. (Glasgow City, North Lanarkshire, South Lanarkshire, East Renfrewshire, West Dunbartonshire etc.)
It's pretty easy to get to Edinburgh from any of these, obviously a longer commute than what it is to get to Glasgow.
If you accepted a longer commute, you would perhaps get a larger property in parts of Ayrshire. It can perhaps be a bit insular in places due to the lack of proximity to the bigger cities, but might serve well if you are finding our wee Scottish houses too small! If you're interested in rural or semi-rural living then it's definitely worth a look.