There is not a great deal to do. Disney it isn't!
You should be able to spend some time along the beach front, visit the pool there, dodgem cars and bowling and stuff.
You could venture out on the train to Stonehaven. Open air pool (heated), and a few things to do and explore.
If you are really brave, you could get the train out towards Inverness, and explore some of the towns along that route.
You could try Storybook Glen. Toddlers delight of Aberdeenshire! Fibreglass figures in a nice country garden. Lots of play equipment and some animals too. Expensive for what it is, but a nice day out when I did it. (Which was one of the warm days we had a few years ago!). I took our own food and glad I did since everything there is N.stle. There are signs saying not to picnic, but what the heck?
We have shops and a bit of shopping. Can't think of anything else, I do not have need to go to the city very often, I prefer Aberdeenshire myself.
Go for it. A change is as good as a rest. It will be fun, as long as your DH has not got to work silly hours.
(this is my second post, would not accept the first one, so forgive the abruptness - I live about 25 miles from Aberdeen).