Geneva for 3 Days

If you're a science nerd, the CERN laboratory gives tours to the public. That's the group that has the Large Hadron Collider. They take reservations only a few weeks in advance.

A short train ride away in Montreux is Chateau Chillon, a terrific medieval castle.

I second the recommendation for CERN and Chateau Chillon - both great places!
Other places I would recommend...
Old Town Geneva - very interesting cathedral that has been excavated underneath. You can explore down to the 1st century...fascinating! Lots of winding streets with antiquarian shops and restaurants. Pretty lakefront promenade.
Lausanne - Beautiful old town that winds up a hill along the lakefront...topped by the old town and beautiful church. Great views over the lake to the French Alps.
Vevey - the hidden gem of Lake Geneva. Very pretty town with a gorgeous lakefront promenade.
Gruyere - famous cheese and a really nice medieval old town with a small chateau you can tour.
Annency, France - not that far away and quite beautiful.
Bring money! Switzerland is a very expensive country and it always seems that Geneva is even more expensive than the rest of the country!

take the ferry trips on the lake, whatever destination piques your interest.

Here's a link for the local tourism website. I think you will find this helpful for your visit.

http://www.lake-geneva-region.ch

If you want to see the amazing sights that Switzerland has to offer then you need to get out of Geneva and head to some different destinations. Geneva is not the quintessential "Swiss" experience you seek.

Thank you all, these are great ideas and tips!