Desktop GUI Gis programs like QGIS are pretty fun and there are tons of resources for learning the basics. You can download elevation raster data and highway vector data for the area around your city or somewhere more topographically interesting and start making maps or just some armchair exploring. Topography and hillshade data are gorgeous. And it's pretty easy to play around with projections, especially changing parameters on standard ones like Lambert.

Another suggestion. Implement the R-tree.