When I was an undergrad from 99-03, the library had stuffed chairs that if you put them front to front, you basically had a love-seat size lounge. Fantastic napping in that orientation.
Central campus on a hot day is pretty fantastic too.
When I was in grad school, my office was part of my major prof's lab, and she let me put a futon in there. That was killer.
Back in the day, they used to have really comfy couches on the main floor of the MU. I think they have kind of ruined those rooms now more as meeting rooms.
Also, most floors in Ross used to have a student lounge in the middle with couches. Not sure if it still does.
Assuming you are not female, great couches near women's room in Ross and used to be in the MU as well.
Seems like there are maybe some couches in the UDCC on the upper floor near the restrooms before you go into the dining area?
The very bottom floor of Howe in that open area they sometimes use as a classroom for the very big classes looks comfy too.
Also fourth floor of the library around special collections used to be good.
This thread just made me sad. Napping on campus reminds me of how I would always see Stevie Hicks napping on the second floor of UDCC. I miss that guy.
I hesitate to tell you this, as it will probably send more people to someone's "secret napping spot", but for CF's benefit...the Browsing Library in the food court level of the Memorial Union has (or at last had) numerous nice couches.
They added computers before I left (-07), which reduced its awesomeness due to the keyboard noise and ruffians who did not appreciate the quiet. They also probably play less Enya than they used to. But still, check there. You also may enjoy actually reading something. Everything from Art History to Calvin & Hobbes to Sherlock Holmes and Plato there.
My FR year (89) I made the investment in a high end Sony walkman that had an alarm...best money ever spent. I'd pull up a chair on 2nd + floor of the library in the sun and put my feet up on the railing and nap away between classes. Sometimes I'd just skip and nap.
Put in a tape with some good music, put on the headphones, and just nap. I think I'll retire in Ames so I can relive those times. A nap sounds good.
There used to be a room in the Library on the second floor that they kept dark and had big stuffed chairs in there. It wasn't high traffic and I used to catch a quick nap there every Thursday between Chem 177L and Chem 177 recitation freshman year. The next year, they turned the lights on in the room and put in those big tables for studying. I was crushed when I found out.
I would suggest finding a spot in the library. Especially near the windows in the sun during the winter time.
If you consider it "on campus", Friley Lounge. I used to just pass out on one of the leather couches after I got done with a food service shift if I didn't have to be somewhere immediately. Couldn't tell you whether those leather couches are still there, though - it's been 10-15 years.
And, as others have said, the library and MU are good options as well.