I think if you go to an Ivy League University in the US it would be a fantastic experience but I'm not sure how a degree from one of the state universities would be received by UK employers.
Between the Ivy Leagues and the state universities, you have got hundreds of other private universities which are highly regarded throughout the world.
Yet having said that, there are many state universities that are world renowned, such as the University of California system, institutions like UCLA and Berkeley (also known as Cal).
In the Times Higher Education 'World University Rankings', Berkeley is ranked #9, there are only two Ivies above it (Harvard at #=2 and Princeton at #5).
The 'World Rankings' of the all the Ivies are: Harvard #=2, Princeton #5, Yale #11, Columbia #12, Penn #16, Cornell #20, Brown #49, Dartmouth #90
Taking into account the lowest ranking Ivy, these are all the non-Ivy colleges that finish above Dartmouth in these rankings (with their ranking in brackets):
California Institute of Technology (1), Stanford (=2), MIT (7), Chicago (9), University of California, Berkeley (10), University of California, Los Angeles [AKA UCLA] (13), Johns Hopkins (14), Michigan (18), Carnegie Mellon (21), Duke (22), Georgia Institute of Technology (24), Washington (25), Northwestern (26), Wisconsin-Madison (27), Texas at Austin (29), Illinois at Urbana Champaign (31), University of California, San Diego (33), University of California, Santa Barbara (35), University of California, Davis (38), Washington University at St Louis (41), Minnesota (42), North Carolina at Chapel Hill (43), New York University (44), Penn State (51), Boston University (54), University of Southern California (55), Ohio State (57), Pittsburgh (59), UMass (64), Valderbilt (70), Rice (72), Emory (75), University of Colorado at Boulder (77), Tufts (78), University of Rochester (=81), Rutgers, The State University of New Jersey (=81), University of California, (86) and Notre Dame (89).
As an American, I would recommend any of the above colleges, all of which would offer any student (from home or abroad) an excellent education and an incredible experience.
There is life beyond the Ivy League. The Ivy League is made up of just eight colleges, so clearly the majority of US students go to non-Ivies, and they seem to do OK on the whole.
It makes me laugh that people here think the Ivy League is the be all and end all. That used to be the attitude back home in the States, but that has changed in recent years, which is why some of the "lesser" Ivies have started to slip down rankings and have been replaced by other colleges.
And no, I have nothing against the Ivy League, I am a proud Columbia alumni. In fact I met my English husband at Columbia, as he had chosen to study in the US, so choosing to attend there was one of the best decisions I've ever made. I'll be honest though, I had another college in mind for the subject I wanted to major in (which at the time was only available in about 20 colleges, but is now more widely available), however it also happened to be the college that my mom was (well still is) a professor at, in the very subject I planned to read. Therefore, I opted for Columbia, as there is no way I could have avoided not having my mom teach some of my classes at the other college!
I just think it's important for people to realize, there are dozens of fine colleges back in the States, which are not Ivies.
NB: One of my younger siblings has just been accepted at Stanford, his dream college, and that's where he'll attend. This is despite the fact he has also received offers from Harvard, Yale, Columbia and Princeton. In the past, people would balk at someone turning down offers from the Ivies, but Stanford (dubbed a "new Ivy" by some) is so highly regarded these days, no-one has blinked at my brother's decision!