If you go to Somerset Apartments they are for non-students. It is at an awesome location at College Avenue and Troutman/Boardwalk. In general, the further south you go in town, the less likely you will find student-only housing. However, you will have to pay for the luxury of not having to deal with parties every night, which is well-worth it! There are several apartments and condos in this general vicinity and it is an EXCELLENT place to reside. You are within walking distance of everything, including King Soopers. This is very handy during blizzards! I lived at Somerset for 4 years and it was my favorite location, although the apartments are not very well kept due to the owner's management.
Another place you can go, if they are available, is the apartments just south of the public library off of Peterson and Olive (just 2 blocks east of College, if I remember correctly). I forget their name, but they are very nice apartments. I lived there for 2 years after college and it is also a great location if you like the thrill of downtown.
The ones near there may or may not be hit or miss. I had a friend that lived behind the old Goodyear Store/Garage for years and she loved it but I never could have lived there. The apartments are around, but you have to figure out if you want a faster or slower pace to your evenings. If you are a social bunny, go north. If you want convenience and more or less quiet, then go south. In general, stay south of Drake, north of Mulberry, and off of Elizabeth to get away from student-only housing.