Hi Jonathon,
The aforementioned Divoká Šárka is worth a trip. The area is accessed by taking tram 26 to its western terminus. The ride takes 34 minutes from Prague's main railroad station (Praha hlavní nádraží).
Another highly recommended option is to spend just 47 minutes on a train from Praha hlavní nádraží to Srbsko, from where you can explore the lovely Český Kras. This is a great place to hike, even if you don't see any birds, and you'll experience a little of the Czech countryside in the process.
http://www.ceskykras.ochranaprirody.cz/index.php?lang=en
Adam
P.S. James, what did you manage to find when you were here?