I actually like flying into GLA directly. AA flies in the summer from ORD. CO has service into EDI now from EWR. At GLA you can take a local shuttle to a local train into the city where you would have to change trains to go from Central to Queens St. Station. Easiest would be to take a taxi - 20 minutes - directly to Queens St. At EDI there is bus to the main station or taxi....again about 20 minutes.

Train from Edinburgh to Dundee is a tad over an hour while Glasgow is a tad over 90 minutes. Service was hourly when I was there. Train station in Dundee is south of town. Airport is west and not as close but not far at all. As for hotel there is an old Stakis that is now in the Hilton chain. It works.