Which would be a better base for touring Scotland? Inverness-shire, Ballater (Royal Deeside), Dunkeld (Perthshire) or other suggestion? These have 2BR timeshares that we could stay in with a family of 5. We would like the see the Highlands, good scenery, such as mountains, etc., castles, and some hiking. We are looking for an area that we can take a few day trips of a 4-5 hour round trip, plus a couple days of close-by things. From Perthshire, we were thinking drive to Glencoe one day, for ex. We would likely start in EDI and end in GLA.
Also, if there is a better base for 4 nights that we could use public transit instead of a car, please suggest.
I'll vote for Dunkeld in Perthshire, though any of these would probably work for you. From Perthshire on a given day you can easily drive north to the Cairngorms, east to Glamis Castle (one of the more interesting Scottish castles to tour), northwest to Glencoe, or west to Loch Lomond (see, for example, the Cruise Loch Lomond website). The Blair Castle website indicates they have activities for kids, though I haven't been there personally.
I shall vote for Ballater because I live only a few miles along the A93 from the village and know it well. Staying in Ballater would make sure you are well placed for the Aberdeenshire Castle Trail and the scenery, whilst not as dramatic as that on the west coast, is still very beautiful in its own right.
This will give you an idea about castles to be visited
https://www.visitscotland.com/see-do/attractions/castles/scotland-castle-trail/
There are lots of day trips open to you within your time frame and Glamis Castle and Blair Atholl are two which come to mind. I've even been to Hadrian's Wall and back as a day trip from Ballater, although I'm not suggesting you do that!
A good website about the Ballater and Royal Deeside area is this one
and an excellent site for walking is the Walk Highlands site, specifically these pages
https://www.walkhighlands.co.uk/cairngorms/ballater.shtml
https://www.walkhighlands.co.uk/cairngorms/braemar.shtml
Hope this helps.