Unfortunately, the train station in Aberdeen is in the least attractive part of the city. (Sorry, Aberdonians, but you know it's true!) The harbour, which is next to the train station, is a fenced in mess of huge oil tankers and container ships, and the occasional Northlink ferry. There are attractive parts of the city (beach, Hazlehead Park, Duthie Park, Old Aberdeen, King's College, Marischal College, Brig o' Balgownie, etc.), but most of the attractions lie outside the city limits. You'd really need to spend an overnight (or more) if you really wanted to have time to explore.
The main shopping street, Union Street, is uphill from the train station. However, Union Street is a shadow of its former glory. Lots of closed down shops, charity shops, and "Poundland" type shops. A few years ago. Annie Lennox (born in Aberdeen) said that she was "...saddened and shocked to see how much decline had taken place." It hasn't gotten any better since.
Having said that, there is a relatively new shopping centre next to the train station. Union Square is as modern as shopping centres get in Scotland, but it's way overpriced.
But you wouldn't be there to shop - just to explore. You can shop just as easily in Edinburgh or Inverness. If you decided to route your travels via Aberdeen, and had only a short time to spend there, my best advice would be to visit Duthie Park, which is actually walking distance (albeit an unattractive walk) from the train station. Duthie Park has one of the most attractive gardens in Scotland, with a gorgeous Winter Garden featuring one of the largest displays of cacti in Britain.
Good luck in your travels!