I did aways at Mayo and U Cincinnati and matched at UT-Memphis. The quality of your letters will depend a lot on your performance on the rotation and your CV and rapport with the residents and Chair. I think you should do aways at places you are seriously considering for residency (one place I really liked asked straight out why I did not do an away there and I don't think any answer would have satisfied them). Also, most of my friends matched at places they did aways at or their home schools, with a few exceptions, myself included.
Mayo is a great place to learn a lot and they have cheap student housing, however they don't seem to mix w/ the rest of the ENT community as much as people at some of the bigger academic centers. Just my 2 cents.
Come to Iowa. We treat you right. Actually, I have no idea if our rotators like us or not, but they usually work pretty hard. We usually get along pretty well with them. I don't know of any who don't match, and many have matched here. Anyway, you probably won't get to know Gantz very well while you're here, but he still might write a sweet lookin' letter!