If you are wanting to travel around, Stirling is a good bet.
From there you can get to:
Edinburgh – 45mins by train / 1hr drive
Glasgow – 45mins by train / 35mins drive
loch Lomond – 45mins drive
Falkirk (for Wheel and Kelpies) – 15mins drive
Perth – 45mins
St Andrews 1hr
You get the idea, it’s pretty central.
In terms of must do’s:
The drive from Stirling to Fort William (through Glen Coe) is a must. the scenery is just ridiculous up there, although you might want to drive through Fort William and continue up the Great Glen to Inverness – Fort William is a dive. You could then spend a night up in the highlands, and come back down the A9 to Stirling – its a bit of a notorious road, but again its stunning on a nice day.
Edinburgh has loads to offer. The castle, Camera Obscura, the National Museum, Dynamic Earth, the Edinburgh Dungeons, ghost tours, Parliament, Holyrood Palace, Arthurs Seat, the Zoo; the list just goes on. You could also easily spend a day just wandering about as it has so much history, and is genuinely a very nice city all round.
Glasgow has the Riverside Museum, and the Science centre – both very kid friendly, but I cant think of a lot else on that side to see (east coast bias maybe?). The Science Centre will easily eat a day, and turn your kid into an over tired monster (but you will all, ages aside, LOVE it).
If going from Stirling you could also include some day trips to the East Nook of fife, St Andrews, North Berwick, Loch Lomond, Loch Katrine etc. They are all easily accessible.
If you base yourself centrally you will have a major chunk of the five star tourist attractions on your ‘doorstep’. However, the trade off is that you will miss out on what the highlands has to offer, but that in itself is another holiday – enjoy!