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What type of design are you trying to do? Like building parts, buildings, construction layouts? If you give more detail I could recommend one of Autodesk's product packages which students can download for free at students.autodesk.com, on their main site though, you can go through there various software and click to get a blurb about what it is used for and some picture examples also.
OH sorry, do you mean for actually going somewhere to study and take courses?
There are a ton of good design programs out there. IF you are specificially looking for design programs, and by design in this day and age you are suggesting interaction design/product design/graphic design, I would suggest going to a school that has both a design program and a engineering/developmental program to facilitate benficial collaboration. However, here is a list of a few good schools off of the top of my head:
University of Michigan
Wash U. in St Louis
Any liberal arts college (Middlebury, Colgate, Bucknell, etc)
...to name a few. Hope that helps.