Pros: Outstanding institution, LOW tuition, excellent faculty, great sports, friendly campus, Honor Code.
Cons: Honor Code (if you don't agree with it), Provo, lack of diversity.
Coming to Brigham Young University from a far more liberal school like University of Oregon is probably something akin to moving from mid-town Manhattan to a monastery... the change is almost alarming at first, but you really get to like the peaceful atmosphere.
BYU is run by the Church of Jesus Christ of Latter-Day Saints, (the Mormons), and I think that fact may scare off many competitive applicants who are not members of that church. That is too bad, since it is a fine institution, and many people would find that they agree with the conservative bent of the school, whether they are Mormons or not.
BYU has very competitive academic standards, and it is not an easy school at which to gain admission. BYU provides a variety of academic offerings, and a world-class faculty in many disciplines. The law and business schools are consistently ranked among the finest in the country.
The grounds are kept in immaculate condition, and the buildings are also always in good repair-- some of them are quite beautiful. Others are in good repair and frankly kinda ugly, being built in a block-like 70's architectural design. Still, BYU's campus is a beautiful and friendly place... visitors may freak out when being greeted on the street by people they don't know, but it's just the way things are at "The Y." The mountains are breathtaking, and loom directly over campus.
In sports, BYU consistently fields competitive teams in lots of sports, and has an active intramurals program. Outdoor activities can be enjoyed during all seasons, and of course the skiing and mountain sports are fabulous. The social scene is lively at BYU, but partying must be kept within the standards of the "Honor Code."
People often wonder about the Honor Code at BYU, which is required of all matriculating students. Basically, students promise to abstain from alcohol, drugs, and sexual relations outside of marriage, and not to cheat. The school takes this Code very seriously, and people do get expelled for breaking the rules. If you can live within these rules, though, BYU can be a great place to go to school, and it definitely isn't boring... although Provo isn't exactly a hip-and-happening hamlet.
Additionally, if you are unwilling to learn about the Mormon faith, you will probably not be happy at BYU (or at least, depending on how easy-going you are, you may be annoyed often). The school requires a religious education element in its curricula, but not all of the classes need to be about the LDS church. Also, many Mormons like to talk about their religion with non-Mormons, so be prepared to learn about it (or how to be firm but friendly in declining). However, people of other faiths-- or, heck, no faith-- can have a great experience at BYU. One of the smartest kids in my high school class went to BYU for his undergrad, and he was Jewish.
Ethnic minorities definitely stand out in Utah County. My wife is half-Vietnamese, and she said that she never felt as much like a minority as she did during the year that we lived in Provo. On the other side of the coin, I work as a college application mentor with inner-city minority youth in Boston, and I can vouch for the efforts being supported by BYU to add to the diversity of their student body. Minority students with solid academic records should consider BYU-- they will have access to excellent support and a quality education for a low cost.
Tuition-wise, BYU is just plain cheap... a real bargain!! Mormon students pay less in tuition because they pay tithes to the church, which help support the university. However, even the non-Mormon tuition rate is ridiculously inexpensive compared to similar private universities around the country.
BYU is a great place to study, and it is a fun place to be a student in a wholesome environment. Frankly, as a practicing Mormon, I would not want to live in Provo forever, but I thought that BYU was a great place to attend graduate school.