Quietest fan for room

Dyson I think makes the quietest fan available but cost $200.00+.
Checking out a fan noise level in a store like Home Depot is not a good idea. The white noise level is probably 60 to 80 DB to start. If you have a DC to AC converter ask if you can take the display model to your car, that may give you an idea of how quiet it is.
Some fans will have a DB rating so check the manufacturers web site for info. Also the less a pitch or angle on the blade the quieter it will be.

Get one of the small split A/C units installed. I am an A/C tech and my wife hates A/C so I put one in my theater-sound room.

http://www.mitsubishicomfort.com/

I would need your room size to recommend unit size. They can cost a few buck but are well worth it.