UCSD is strong across the board. It’s well-known for strengths in STEM, but it has world-class faculty in every discipline.
You can’t transition to law as an undergrad. Anywhere (in the US). You can choose majors that are law-adjacent, like politics, public policy, economics, and history (anywhere). Arguably any discipline that interests you is law-adjacent, because there’s no pre-law major. I doubt the majors you’ve chosen at UCSD are binding – humanities majors usually aren’t, and it’s generally pretty easy to explore new fields. This page explains the major choice and selection process: How to Declare or Change a Major (Undergraduates)
I understand the temptation to go to NYU, but are the costs and delayed start worth it? I even understand the temptation to explore someplace other than California (I am from SoCal, left for college, and never went back). But you can go to the Northeast for grad school, or you can try out a career there. This won’t be your last chance to do that. But if you take on enormous debt, you’ll find yourself with very limited options after college.