Depends what you want to do and how much time you have.
Eg it is possible to go as far flung a places as Shetland or Orkney, the outer and inner Hebrides without a car and have a great time and see loads.
Edinburgh is pretty, has the national museum and galleries, its castle, Holyrood and the parliament.
Glasgow is loud and has museums, galleries, architecture, shopping etc but has a distinctly different atmosphere.
Dundee has the Discovery.
Aberdeen has mutant seagulls, but not much worth visiting really. Inverness is pretty, not much to do in the actual town but lots of places nearby to explore such as loch Ness and Aviemore.
Stirling has a good castle.
Skye can be got to by bus, lots of nice walking as well as the scary stuff on the Cuilin. The Hebrides are wild but friendly places. Shetland is interesting, some impressive coastal landscape, good bird life. Orkney has amazing history, and good wild life.