If you’re thinking of spending a week in Edinburgh then Arthur’s Seat is a nice gentle hike for kids of that age. Obviously there’s THE castle, but there’s also Craigmillar Castle that’s outside the city. That’s one of our favourites. Will you be hiring a car? If so, it’s really easy to get to. I’m not very knowledgeable about buses.
Point to note that can be disregarded if we have ‘normality’ by your trip, but lots of historic sites that are about to reopen are putting booking systems in place to limit visitor numbers. This includes Edinburgh castle, Craigmillar, Stirling and some other places that I’m likely to mention in the rest of my reply. I hope that’s all finished by the time of your trip, but it’s worth being aware that that’s the current situation.
It would, but there are also direct flights from Edi/Gla too.
I don’t think you’d need to spend more than £100 per night anywhere in Scotland. Obviously it depends on the style in which you’re accustomed to, but I would think something like £80 or £90/night would be reasonable for Edinburgh and £70-ish/night for Inverness.
I think your personal preference on moving around will dictate this, but here’s are some thoughts…
So if you spend some time in Edinburgh, say up to a week, then move around (you also mentioned Glasgow), so maybe you could spend some time at the West Coast. You can easily visit lots of islands from there and maybe just do a day trip or two into Glasgow. I’m not sure that Glasgow has quite as much for the little ones as Edinburgh (I’m thinking of attractions in Edinburgh like Camera Obscura and Dynamic Earth and can’t think of equivalents in Glasgow).
From the West coast you can visit some lovely islands like Cumbrae (where you can hire bikes and cycle around the island) or Bute (where there are some lovely walks with great views and a putting green). The coastal towns, like Largs Dunoon and Oban, are lovely too.
So it might be too much, but a 3-way split stay between Edinburgh, West Coast and North would be ideal. If you don’t want to move around that much, then you’d maybe need to sacrifice some of your exploration for travel time.
Is Inverness set in stone? I wouldn’t try to put you off going there, but if it’s islands, hikes and lochs you like, then I might suggest trying a couple of nights on Skye.
Again, not putting you off the Highlands, but you don’t actually need to head that far north to get beautiful scenery etc. Anything north of Stirling is dramatic in landscape. In fact, I have some lovely hills right here in West Lothian!!
Blackness Castle is great fun for kids. It’s the one I live closest to. I believe they pretended it was Fort William in Outlander.
There are some great nearby historic properties (Linlithgow Palace and Loch Leven Castle ((a short boat trip across the loch to its own Island))) if you headed out that way. Again, those kind of places are probably best and easy if you have a car, but they’re awesome for kids.
I feel like I’m rambling, but I hope something in there helps. If anything I’ve said needs more clarification, just ask.