In reply to briansy:
As a lot of people have said, hiring a bike opens a huge number of options, especially around central Cairngorms.
Longish day without a bike but loch Avon slabs are an excellent day out if dry and the alt garbh mor not in spare!
From ballater directly coyles of muick is a superb short day with awesome views down deeside to bennachie and up glen muick into main Corrie of lochnagar.
Similarly, Geallaig hill from glen gairn gives lovely views for a lower and shorter day.
Lochnagar it's self obviously, but I generally prefer to either bike to geldershiel bothy and up from there via west ridge or the stuic (easy scramble), or walk in from keiloch and back down over the north top and via the prince's stone. Takes in some lovely old Scots pine woodland. Though the white mounth circuit from Glen muick is a really nice day out. Again, with bike you can cycle to Glas alt sheil, and head up the forked lightning path to broad cairn and finish down the via glas alt shield waterfall back to bike and cut out a load of landy track trudging.
Beinn a bhuird, especially with a bike too - dividing buttress as an excellent scramble from keiloch, or bike in to bulig lodge ruins and make a circuit over Ben Avon and Being a bhuird. If time allows dropping down the ridges running NE after east meur gorm craig takes you through lovely torrs.
Less inspiring maybe but walking direct from ballater to mount keen via glen muick house path is a nice non-driving option.
Again, better with a bike, but cairn an t-saigairt mor from callater lodge, then looping in as much of white mounth or glen shee hills is a nice day out too.
I've not suggested stuff out towards braeriach as kept more to the braemar side, though loads out that way especially with a bike!
I can also heartily recommend the highland bakery at crathie - best butteries in the shire and rest of their cakes etc not too shabby either 😀
Happy to give a few more route specifics if you're keen on any of the above.
Cheers,
Stu