Students with these interests also may want to consider a major in public policy, which relies on the fields of political science, economics and philosophy for its foundation.
Look at Occidental, Santa Clara, University of San Diego and Loyola Marymount (LMU) all California schools and all near or in an urban area. The Claremont Colleges as mentioned above are an excellent option also.
Your goal should be to have a balanced list…some reaches, more matches, and at least one affordable safety (2+ if you want to make sure you ultimately have a choice).
Barnard is a reach, do you have schools in the other categories too? What is your affordable safety?
Is Barnard affordable per their NPC?
Other potential schools: Trinity (CT), U Richmond, UC Davis, and Lewis and Clark, which have the advantage of being in (or close to) state capitals, which appeals to many students looking to study poli sci.
If cost were an issue, look to Arizona and the Honors College.
You have lots of great suggestions already on the West Coast- I’d add Willamette, Puget Sound, etc.
You mention New England or the West Coast but Barnard (in neither) is your top choice. So we’ll stick with the NE in general.
Wesleyan, Union, Trinity, and Connecticut. Since you are applying to Barnard, how about Mount Holyoke and Bryn Mawr ¶.
I’ll add - not West Coast or New England - but U Denver for mid size and Macalester in St. Paul - which would fit your bill.
It’s really a question of where you want to go - so start researching. Sounds like the LACs are right for you but perhaps if cost an issue, a big state school Honor’s College works.
Since UC’s and CSU’s are test blind, having no SAT/ACT will not be a deterrent however with some of the other schools, SAT/ACT scores can definitely help your chances.