So having attended an Ivy, and knowing lots of other people who did, I can tell you they are in fact just colleges. They are certainly well-resourced colleges, and if you can comfortably afford one and it otherwise fits your needs and preferences, it can be among your good options. But there is nothing magical or unique about them, they are just colleges.
And for the record, they do not have a monopoly on kids from important families to network with. More than average proportionately? Sure. But there are kids from those families also going to a variety of other colleges.
OK, and then what does “equivalent” really mean? The Ivies themselves are pretty diverse, and so a college “equivalent” to Cornell is not necessarily “equivalent” to Dartmouth, or vice-versa. And so on.
And then some people would assert Georgetown is not “Ivy+”, but then Georgetown is often the top choice of kids who specifically want to be in DC, say because they want to be plugged into the DC political and public policy scene. It is indeed also one of those non-Ivy colleges where lots of kids of important families will be attending. I’d suggest you reflect on how liking Georgetown, quite reasonably, just shows letting a regional sports conference like the Ivy League dictate your sense of what colleges would be best for you does not make much sense, even by extension.
So I would take a step back and think in more fundamental terms. If you in fact get into Florida and it is free, what would you really be looking for out of a college that might cost a lot more? Just using Georgetown as a model, is it some specific locational ties, like Georgetown with DC? A smaller college with smaller departments and smaller classes? A specific sort of academic program (like would you be looking at SFS)?
Then this can guide you to interesting options to consider. Like, a lot of people who are interested in Georgetown, particularly SFS types, also end up interested in William & Mary. Despite being a public university, it is a smaller college than most publics, it is extremely strong in political science/public policy/IR sort of programs, and it is also very plugged into the DC scene. It also has a really cool dual degree program with St Andrews in Scotland, where you spend two years in each place, which could be a huge attraction if you are at all interested in the idea of international networking (St Andrews being a great place to meet the kids of important families from all over). SFS types would probably do International Relations both places, enhancing this effect.
Of course you can go to William & Mary without an interest in St Andrews. But my point is if you are looking for things Florida does not do that might be worth considering as special opportunities, you can look for things like that.
But to be blunt, I don’t know a lot of kids doing a thoughtful application list who end up looking at both Georgetown and, say, MIT. There is very little overlap in strengths. So understanding why Georgetown could also help you understand why maybe MIT isn’t a very logical choice.
And so on.