Loads of good places to run but dog off lead and good surface might be tricky.
Depending on tides you could run along the beach and loop back through Seaton park/river Don path but need to deal with a bit of traffic. There’s a good path next to the beach too
Hazlehead park and Counteswells forest also an option on edge of the city. Lots of other walkers and cyclists likely though.
Kirkhill forest near the airport is worth considering but quite hilly. It’s off-road but pretty well surfaced .
Duthie park and old Deeside railway line are good but quite busy with other users so dog off lead would be a bit inconsiderate.
if you don’t mind a bit of a drive Glen tanar is beautiful and great for running but it is off-road.