Hi, Christina,
I'm sorry that you couldn't get any closer than Pitlochry or Ballater for the Braemar Gathering. As of last week, there were still some rooms available in Banchory, but they're probably gone by now! Ballater is a charming town, and if you enjoy hiking, there are lots of good hikes in the area.
As you're going to have a couple of nights in Aberdeen, why not do that first, then stay somewhere along the coast? Given a choice between Arbroath and Montrose, I'd probably opt for Arbroath. It has a great little harbour, a really good walk along the cliffs, the Abbey where the Declaration of Arbroath was signed in 1320 (supposedly the inspiration for the US Declaration of Independence), and several places where you can purchase Arbroath Smokies! Cel's on Ladybridge Street is a personal favourite - smokie pies to die for!
Other coastal choices would be Cruden Bay (north of Aberdeen) or Stonehaven (south of Aberdeen). Both have places to visit within (and without) their environs. Cruden Bay has Slains Castle and the Bullers of Buchan; Stonehaven has nearby Dunnottar Castle, which you definitely do not want to miss on your way south. All of these can be visited on half day trips from Aberdeen.
A lot will depend on your interests. Certainly Pitlochry and Ballater would be worth two nights each, but you need to find out what other places are nearby which pique your interest. If castles are your interest, there are more concentrated in the Aberdeen area than anywhere else in Scotland. You could base yourselves in Aberdeen and spend several days visiting castles and gardens. If nature is something that you enjoy, there are the seals at Newburgh and the amazing bird covered cliffs at Fowlsheugh, just south of Stonehaven. Perhaps you could do three nights in Aberdeen and one in Arbroath on the way south to Edinburgh.
Please keep asking questions. We're happy to provide answers!
Best wishes, and safe travels!
Mike (Auchterless)