Every so often, one hears a current or former student of a non-Ivy League school refer to their college/university as being part of the "Ivy League of the ..." [fill in the blank with geographical term other than "East" or "Northeast" -- e.g. West, Rocky Mountains, Dakotas, -- or the name of another country/continent or another descriptive term*].
I personally do not know of any circumstances in which this has produced the desired impression, which presumably is something on the order of "You may not know much about my school and may not even have heard of it, but it is a really really good school and you should be impressed." It may well be a (very) good school, but if someone isn't familiar with it already, there's not much you can do at this point.
Another inadvisable approach is to mention a famous person who graduated (or briefly attended) your school. This, at least, is a factoid rather than propaganda, but should only be used as an 'interesting trivia' kind of conversational element, rather than an attempt to impress.
Students and graduates of certain small liberal arts colleges may find that their schools are not as widely known as they had thought/hoped, no matter what the ranking of the school in US News & World Report. In this case, it is best to accept this fact and come up with a brief but informative description, even if only to mention that it is in Massachusetts or Ohio or California.
Alternatively, when talking to someone who isn't well informed about your school, you may know from experience exactly what you need to say. For example, my friends from Vassar College say that they still have to explain that Vassar is not a women's college and has not been for nearly 40 years, and my friends from Cornell College are perpetually explaining that their school is in Iowa. And a certain person who went to Smith College, when confronted with the need to provide further information, likes to say "The "p" in Psmith is silent" (literary allusion few people get but she thinks it is funny anyway).
If you're going to do the "Ivy League of the Whatever" thing in conversation, at least choose your audience. If you say this to a group of students/graduates of schools that don't use this description, you might come off as kind of a jerk. If you say it to an advisor or potential advisor, they will already have their own opinion of your school, and the news that your school is Ivy Leaguesque will not impress. Presumably your own abilities and/or potential will impress or not, no matter what school you went to.
So, to whom can you mention the Ivy League of the Whateverness of your school? You do have some options, including fellow alumnae/i, your parents, and most small mammals, though even among these, not all will care.
* e.g., Women, Tundra, Interstate 5, Latvia
9 months ago