Columbia vs. Williams vs. Amherst vs. Yale

First of all I know that there are forums similar to this and I have read most of them; however, I still would like some personal advice tailor-made so I can get a better understanding. I posted this on the Williams thread but I would also like to see the perspectives of people from Research Universities. So I am a prospective student at each of these schools and have received early writes from all of them, except Yale which I hope to get accepted to. I am a History major and have an interest, possibly as a double major, in film and media studies. I would also like to get into politics in the future and my dream is Yale Law School.
In terms of my academic fit, I believe that I would perform better in the close-knit community of liberal arts institutions such as Amherst because coming from a low income background I would appreciate the extra support that I never had. However, the grade inflation at the Ivies might be able to counter this; Yale has a 3.51 average GPA! I truly enjoy history and I know that WIlliams has one of the best Art History departments in the world. I personally think that I would enjoy the academics at Williams the best.
Amherst has a fantastic film program with Mt. Holyoke where one can actually intern and make films. As for the area, none of these schools have a location that can compete with New York City. I don’t think I would dislike the rural area of Williams, but I come from a large urban area so I would feel at home in New York. As for Columbia, since it is located in New York City, I would love to intern for Hillary Clinton if she were to run for President in 2016 and since her campaign would be located there that would be a fantastic opportunity. New York also has a great film scene (Spike Lee or Martin Scorsese might be right around the corner).
Since I would like to go to Yale Law School, I wonder if attending its undergraduate institution would give me a small bump. Yale also has a study abroad program with the University of Tokyo that only one other school, Princeton, has and it has been one of my aspirations to live there for a while. When I look at the statistics on Parchment, I see that students select Ivies in general about 80% of the time in comparison to selecting top LAC’s such as Williams or Amherst. Am I missing something? I don’t really care much for the prestige when speaking to the average layman, even if my family would rather me attend UCLA for those reasons but that is another story. However, I am concerned that perhaps attending Williams or Amherst might hamper the possibilities of me getting into politics. Is this true? I don’t think it is but that is the impression I get. I understand that attending these strong LAC’s wouldn’t reduce my chances of attending graduate or professional school but is the alumni network strong enough to be able to bolster me into politics? I would really like to become a member of Congress in the future. I am very disappointed by the fact that Williams and Amherst have their visit days on the same days so I have to choose which school to visit. This is a very hard decision to make! Anyways, I read forums on this website a lot because students at my school never go any higher than UCLA so I appreciate the insight it has given me. Thank you for reading this, if you did. All advice is welcomed!

First you have to decide whether you like small liberal arts colleges, or large research universities. Then you have to decide whether you like a small rural town or a large major city. There are advantages to each situation. Someone may thrive at one, and absolutely hate the other. I would recommend visiting places you are interested in.