A good anotated list of textbooks on geometric measure theory can be found in this blog post. Besides comments on Federer and Mattila it has several more examples.
As my personal favorite I found, while lecturing geometric measure theory, "Measure Theory and Fine Properties of Functions" by Evans and Gariepy. It is short and crisp (often you have to build the geometric intuition on your own, but that is ok with me) but the proofs are pretty detailed. Also it contains most things I am interested in. However, for covering theorems like Vitali and Besicovitch, I found Krantz and Parks "Geometric Integration Theory" a bit better organized. Mattila is better suited if you interested in Hausdorff measure and fractals. If you want to know if a certain theorem holds in the case the measure is defined only on a metric space, a Hausdorff topological one or what happens when separability of the underlying space is lost, Bogachev's two volumes on measure theory are the place to look (although, there is not so much "geometry" in there).