I've recently completed a paper detailing the design decisions made in Cabri II Plus, Cabri 3D, Geometer's Sketchpad 5, Cinderella 2 and GeoGebra, to be published later this year by ZDM. On this basis I would be reluctant to recommend GeoGebra.
It really depends what is meant by undergraduate geometry, however, and what your expertise is with software. Cinderella is the most powerful of the programs above, as it incorporates a programming language. It also will represent hyperbolic and spherical geometry as well as standard Euclidean geometry. Cabri 3D is best for 3D geometry. Sketchpad is increasingly creating learning materials geared to university level mathematics.
There are also of course Maple and Mathematica, which your institution may already have. I don't know a lot about the geometric capabilities of these programs, however - but certainly they are currently the most powerful for analytic geometry.
There's also Autograph, not as powerful as Maple or Mathematica, but perhaps easier to use.
Let me know more about precisely what is involved and I will try to be more specific.
Kate