Rice is a very good school, one of the ten best in the country. A plurality of its student body comes from within Texas, however, as opposed to many other top schools, where no state has any solid majority. Less than 10% of the students who attend Harvard come from Massachusetts, while 40% of Rice’s undergrads are from Texas. This comes from the regional draw and name recognition.
There are a great many schools in the country that are very good, but only a few which manage to be both very good and famous. Not every school which is very good is famous, and not every school which is famous is very good. The University of Alabama is famous for football, and while their academics are solid, they are not in the top tier of schools. Conversely, Rice is a very good school academically, but is not nearly as famous.
These unfamous schools experience regional draw, where the students who know about them the most are the ones who live nearby, often in the same state. The top students in Texas will apply to the famous schools, Ivy League, Stanford, and the like, but most will also apply to Rice, and those that don’t get into the Ivy League will often attend Rice.
This system is neither good nor bad but serves to illustrate an important point: that you should do your research well when deciding where to apply to colleges. A school may be famous, but that does not mean it is the right fit for you. What any given student needs from their college experience, and what a school is capable of providing, can differ greatly. Look at the schools you apply to, and you will find one which suits you well, regardless of how famous it may be.