Thanks! I'm probably going to end up at the Academy Plaza on Findlater Place, on the basis that it seems cheap, non-scummy, central, and on the airport bus route. Any vague directions from there would be much appreciated!
(And sorry if I was unclear, by "whistlestop tour", I meant me having a potter round by foot and/or bike, not an actual tour...)
And a bit of rain won't put me off - I'm from the West of Scotland...