Well,I am currently doing My Master in Aberdeen medical school,The medical school is in Foresterhill as you probably already know by now.
Since it is just one year program I can't pretend I am the expert,there is plenty of different places out there.
But quick information
1-Many if not most student accommodations are around Old Aberdeen,it is close to the University Campus and Sir Duncan Rice Library which is an awesome place to study specially at night (close at midnight except weekend at 10pm,and in exam period it opens 24h) though many medical student prefer to study at medical school library.
2-In general old Aberdeen is the coolest place in the city IMHO,and there is a a University bus from Sir Duncan Rice Library to foresterhill .
3-That said student accommodations are usually most expensive,from what I know rents has gone down in the past month,the cheapest options are usually a private flat that you share. I think you can get a 2 room flat and after bills it will cost you like 700 pounds,when paid by 2 ppl that 350 which is less than any student accommodations. You can get such price in foresterhill easier I think,if you know someone doing a degree their too you can be flatemates