<p>Not knowing anything more about the OP, I personally don't see an obvious choice. All three are fantastic schools and none of them are total misses on any of the OP's criteria. </p>
<p>A few thoughts:</p>
<ul>
<li><p>Williams and Carleton are both fairly rural, but Claremont is an urban-y feeling suburb. All three campuses are quite residential, but do you have a big location preference?</p></li>
<li><p>Weather. Not everyone prefers SoCal sunshine, so my point isn't that any one is objectively better, but you are down to some extremes! You're obviously used to MN winters, so are you someone who handles them just fine, or does a change in climate really appeal to you?</p></li>
<li><p>Ease of travel. Carleton should be easy for you to get to. Claremont is an easy trip, but a relatively lengthy/pricey one. I've never visited Williams, but I'm told that it's tedious to reach. This was never a factor for me, but a lot of people on CC weigh it heavily. Just a thought. Tied into this is distance from home. Are you comfortable heading towards one of the coasts, or would you prefer to stay near home?</p></li>
<li><p>Social atmospheres. From what I understand, all lively, but very different. </p></li>
<li><p>I do know multiple Mudd students who've studied abroad, but it's not very common. I don't know whether that's due to lack of interest or lack of ease, but that might be something to look into (then again, if you know this early on that you want to study abroad, you should really be able to make it work). I've heard from the director of off-campus study that they're really trying to pump the program. </p></li>
<li><p>Mudd has a tech-y atmosphere that Carleton and Williams lack. Yes, you can easily meet students from the other colleges, and there are also plenty of "normal" Mudders, but the tech school atmosphere definitely does prevail. That might be a selling point or a turn off, but regardless, it's a big difference. I don't know much about Williams, but based on what I've heard, the schools probably attract very, very different (although incredibly intelligent in both cases) students, and I imagine that Carleton falls somewhere in the middle. Maybe that's a false impression, but to echo a previous poster, have you visited? What do you want in your peers? What's your ideal social scene? What's your idea of a fun dinner table conversation?</p></li>
</ul>
<p>The good news here is that you have no truly bad options. None of the schools should prevent you from pursuing your stated interests, and clearly, there are reasons that you're very drawn to all three. I think that at this point, you can start putting a greater emphasis on "soft" factors, because those are where the biggest differences seem to lie. Just my opinion.</p>
<p>Final decision time is stressful, but you're in a good position. Best of luck :)</p>