What would be the best college to go to if you want to design games and play games

University of Utah has a great video game development program. I work with a graduate of that school and through him have learned much about the program. Not only do they teach relevant skills, they work hard to get their students involved in real world projects.
There is also Digi-Pen, which is more like a trade school than a University. I have also worked with a graduate of that institution and believe that it's program is rigorous and complete.

In the end, though, any University with strong technical and fine arts departments will serve you well. I studied Mathematics and Physics at Montana State University and learned programming on my own and I have been a professional game developer for more than 20 years. The trick is to study subjects that teach you problem solving and to make games -- whether that means modding existing games, writing your own from scratch, of building levels for something that already exists. Work hard, don't be afraid to fail, and be ready to put yourself out there when opportunity knocks.

Good luck!

Not sure there is one right answer for everyone! There are a lot more choices now then there were just a few years ago.

You need to do your research and ask the schools you find for info and see if it looks like they are teaching you the skills you think you'll need, if their presentation methods match your learning style (on site, or online for example), and what success they've had so far. Ask if they have any successful graduates. Reach out to grads and former students online, to see if they had it all over again, would they recommend their school to you..