It seemed to me that BYU can’t quite grasp the concept of anything outside Mormonism, let alone atheism. For example, you need an ecclesiastical endorsement from your local bishop or, if you’re not Mormon, the equivalent in your own religion. No provisions given on what if your religion doesn’t have an organized leadership structure, let alone what if you don’t even have a religion. I got mine by visiting my local Mormon congregation and talking to the bishop there, which sort of defeated its purpose (the Mormons have a very close-knit community; the local bishop is supposed to already know the person who’s seeking the endorsement and able to judge whether that person is of good enough character for BYU).
Personally, I don’t see any benefits from going there from a religious vs. non-religious viewpoint. It is very, very Mormon, so you’ll definitely learn all there is to know about their beliefs. As for being treated like a freak or being bombarded with conversion attempts, it really depends on the who you come across, as well as how much and how deeply you are willing to socially interact with them. I’m a massive introvert with huge social anxiety issues; I didn’t mix around much and so I never really felt pressured to convert nor was I ever ‘treated like a freak’ (well, the people there are really nice, so I doubt they would have anyway).
The main benefits of going there are the low tuition as you’ve already mentioned, and some really good degree programs (most of the business degrees, animation… I’m sure there are more worth mentioning).
And regarding whenhen’s post above, I always felt it was better to be a total outsider (i.e. non-Mormon) than to be a less active Mormon in BYU. We aren’t held to the same standards. Well, officially, the only difference in standard is you wouldn’t be expected to attend church every Sunday; but from a social standpoint, I felt easier about being myself without being judged. For example, I could announce to friends that I just drank coffee and they’d laugh, whereas a Mormon might not do that for fear of being ratted out.