This question has been on my mind as I am approaching graduation. It is a difficult question to answer, but I will present my thinking on the issue. I had a choice between attending the SFS or the University of Virginia, which would have been cheaper as an in-state student. So, my analysis assumes SFS versus a state school. Also, it only applies to undergraduate education.
The core curriculum can be readily replicated at a state school with the notable exceptions of Map of the Modern World and the foreign language proficiency exam. However, it should be easy to find a close approximation of the Map class at most state schools, and while most schools will not certify proficiency in a foreign language, a student can simply take a foreign language class every semester.
Once a student gets into a major, many of the classes are offered only at Georgetown. Yet, an IR concentrator in a political science major or an econ major focusing in international economics at most state universities should have enough choice of classes that this is not really a big deal, but it depends.
There are some things specific to Georgetown that make it unique. First, you will attend school with a lot of really smart people who are interested in international affairs. This has definite benefits, including the ability of Georgetown to offer esoteric international relations classes. This would not be possible without a critical mass of interested students. Yet, these benefits are difficult to quantify on a cost-benefit basis. It ends up being a qualitative judgment.
Second, Georgetown also benefits from its location in DC. Internship opportunities in international affairs abound. A summer internship is definitely doable for state school students, but being in DC is a definite plus.
Third, job opportunities are another benefit. The international affairs community knows that the SFS has a lot of smart kids interested in international related jobs. So, more international affairs job opportunities are presented at Georgetown than I have seen at other schools.
Fourth, foreign language classes are designed to make the student proficient. They are not just reading and writing classes, but also focus on speaking and culture. Furthermore, almost every language offered has enough classes to reach proficiency. For example, Chinese, Arabic, Russian, and other hard languages are offered intensively over three years to reach proficiency before graduation. Universities that claim to teach more languages frequently offer only a year of instruction in many of the languages. Georgetown offers three full years in all, or at least the vast majority, of the languages.
Last, Georgetown SFS alumni are in every conceivable field of international relations. I have found them to be very responsive to questions about careers, if you email them. Again, this is difficult to quantify.
In conclusion, I think a student could recreate a course of study at a state university that approximates most of what is offered at Georgetown SFS. However, they would not be able to take some specific, esoteric classes and would lack the other benefits listed above. Whether these benefits are worth the cost savings of going to a state school is an individual judgment. If the student is very interested in a specific aspect of international affairs and becoming proficient in a difficult language, then I would say it is most definitely worth it. If the student is only interested in something generally international, then a undergraduate degree from a state school followed by an MA in IR might be better. That way the student could discover whether international relations really interests them, and what particular aspect or aspects they should pursue further.
If you are looking for an opinion regarding the rankings of international affairs schools, mine is here.