Go West, young lady! West!
You can get to the West Highlands very easily. Cowal is nice, or Oban (not IN Oban, but surrounding area.
A little more driving (from Edinburgh, maybe 4 hours) would get you to the real North-West - Gairloch, Ullapool etc and it is brilliant.
Islands are also a good option - Mull has been mentioned but Arran is also fantastic. Inverness shouldn't be much more than 3 hours from Edinburgh if you get a clear run up, and there are places in the Highlands before there which are good too - Carrbridge, Grantown-On-Spey, Aviemore.
Don't rule out not-so-distant Fife, especially St.Andrews, and the East Neuk.
We tend to go further - we have a house in the Outer Hebrides but that is a lot further than you would like to go - it is roughly 10 hours door to door for us including 3 hours on the ferry, check in time, stopping at Burger King to placate small children, toilet stops etc. It is SO worth it though, maybe when your kids are a bit older?
(live in Scotland, always have pretty much, holidayed in Scotland as a child all the time. Still do!)