I live in Aberdeen and would suggest heading out to Aberdeenshire if you can. If not old Aberdeen and the beach area, especially fittie (Foot Dee) is nice. The city isn’t what it used to be and some bits of it are pretty dire, unfortunately the bits closest to the port! It’s 100% worth it to venture out - I love Stonehaven personally, can very easily get a train there and back, but have a plan for once you’re there if you have mobility issues as the station is at the top of a steep hill which will be a bit of a walk (about 20 minutes). If you do go and can manage hill walks there’s a great walk to Dunottar Castle from the beach which has amazing views, the beach is lovely and I’d highly recommend Aunty Betty’s ice cream shop and the bay fish and chip shop.
I really hope they start doing cruises from Aberdeen - driving down to Southampton is a long trip at present!
To answer the question though, Aberdeen port says they do shuttles but it is walkable if you want to walk.
