I wonder whether Igor Pak's "Lectures on Discrete and Polyhedral Geometry" might be appropriate as a textbook for an undergraduate geometry course. This is still in preliminary form, available on his website. In the introduction he describes a selection of topics from the book that could be used for a basic undergraduate course. There seem to be lots of exercises, and at a quick glance a lot of the topics look quite interesting. This whole subject is way outside my expertise, however, so I have no idea if the book would make a good basis for a course like the one you'll be teaching.