All 4 are great schools but very different. Williams and Bowdoin are liberal arts colleges, while Rice and Wash U are research universities. The focus at Rice is mostly directed towards the undergrad program, while Wash U has a law school etc. From your posts, it sounds like Bowdoin might be the best personal fit for you, but your parents are pushing for Williams. I assume all of the schools are equally affordable. You should focus on where you would feel the most comfortable for 4 years. Big city, small town, or remote location.
It sounds like you have written off rice. Although many students at Rice are STEM focused, there are many social science majors also. Rice is in the process of building a new Social Sciences building. The Rice political science program is very strong. Rice is located in Houston which has lots to offer in terms of culture, great restaurants, shopping, professional sports teams. Rice gets high ratings for quality of life and happiest students.