The Institute of Design (the graduate design program at the Illinois Institute of Technology) in Chicago has a rigorous program (actually, several different programs) that also accomodates (and requires, I believe) non-designers with an additional 9-month "Design Foundations" program that precedes the master's program.
It's well respected and outputs good critical thinkers. However, like ANY design graduate program, you will not get the immersion in pure, hard skills that you would through an undergraduate design program. There's no subsitute for an undergraduate program's 3-5 years of continual practice, critique and correction. You will approach some of those skills in a graduate program (but not all, and in limited exposure), and the problems you handle in a grad program will be meatier, more process/experience/strategy-based, more difficult, more interdisciplinary, and involve more teamwork vs. individual work.
The graduate vs. undergraduate question has been addressed and discussed many times in many threads on the Core77 boards; searching for them might help you as well.
Full disclosure: I am a graduate of the above program, though I knew I would not learn a lot of "skill-based" things there (like sketching), so I preceded my graduate work with two years of undergraduate ID study.