As the official spokesman of the 'Away Rotations Are A Waste Of Time Club', which, at this time has a total of one member, I'd say only do an away rotation at a place that is very convinient (and cheap) for you and somewhere you probably will really want to go. If, however, you are deciding between an anesthesiology away rotation and a rotation that is likely to be fun or something that you'll likely never do again, I would go for the later. Away rotations, in my unsupported oppinion, don't make a bit of difference to matching unless you're a very borderline candidate...and even then I still think the obligatory interviews you get are unlikely to yield much. I'll even go further by saying that if you are seriously considering doing more than three away rotations in anesthesia (in addition to your home rotation), you're nuts...you'll be putting people to sleep for the rest of your life.
Also to answer your question: Do you know of some hospitals that will accept students into their residency program with only an interview?
The answer is yes, most certainly all of them.