If you liked Barnard, you might like Bryn Mawr. Visit the website and read about the major in Growth and Structure of Cities. Here is a link: https://www.brynmawr.edu/cities/
Your reasons for transfer are solid. Go ahead and make some applications. If/when you get your acceptances, that will be the time to decide whether to stay or leave.
I think that it is difficult right now to find a good LAC that doesn’t have a majority left-of-center student body. Also, given the cost of private education in the US, the LACs have many more students from upper income backgrounds. If you want a broader mix of economic background and political orientation, then you should take a look at public universities. Which ones have some kind of recognition in your country (for a first job out of college)? Which ones have strong Urban Studies programs (for your possible major)? Could any of the various branches of City University of NY work for you? What about Temple in Philadelphia or Rutgers in New Jersey?
If you focus your possible transfer list on that major, I think you might find places that work for you.
Wishing you all the best as you work through your decision-making process.