I know the poster has already decided, but figure these all have posterity, so may as well throw in my analysis. My post and this analysis mainly focuses on the career side of the equation but I think it is really misguided to focus just on that! Personally, I think going to business school and just caring about career outcomes is missing the point that you need to learn and grow in other ways! The culture and experience needs to be weighed just as much (though the weighting is very personal and thus why I think no one can tell anyone what they should choose). And, the average student only keeps their first job for two years, so these other things matter a lot...
I think it is misguided to automatically say that if someone is interested in finance, Stern is the clear choice. It is important to not confuse finance or investment management or private wealth management (the poster's intended career interest) with investment banking. Stern's finance recruiting is dominated by investment banking; in the 2018 career report, 26.2% of Stern students overall went into investment banking. The poster was interested in a subcategory of investment management, which I believe is captured within the "Finance-Other" bucket within the industry classification, which is 0.9% of students or 3 students (that is the combined total for asset management, private equity, and hedge funds). Now, there are always funny things going on in these career reports in terms of classification, but if you look at the Function classification, they do have a Private Wealth Management (essentially being a financial adviser for Merrill or Morgan Stanley, etc. or working on that side of the business) breakout and that is 1.5% of students (or 5 or 6 students on my math). That said, Stern has lots of alumni that eventually end up in these other roles (but don't initially as they don't have the backgrounds and thus do banking first).
This means that it is quite rare to do something in finance outside of investment banking even at a "finance" school like Stern. As such, on campus recruiting will be very rare and you'll mainly need to be self-motivated. A lot of finding job postings, reaching out to alumni, etc. Expect the career office to not really be that helpful in these types of searches. Being in New York likely makes it marginally easier to meet people in person as otherwise you'd be getting on the phone and then flying to New York (or other cities; I know some Ross people work in PWM at GS in Chicago) to meet in person. Geography is important; for PWM, it is not solely about NYC, so if you want to end up in another office, that is something to consider (78% of Stern grads remain in the Northeast or basically the NYC-Boston corridor). For investment management (essentially the institutional side), the largest concentration of big funds is in Boston (by far the leader for the massive funds), LA, NYC, and San Francisco with big presences in cities like Kansas City, Baltimore, and Denver.
For what it is worth, Michigan gives less detail on the specific finance career paths, but it looks like 8.4% of 2018 graduates went into investment banking (they had others who went into other areas of finance but not enough to call out the specific areas). This is probably a function of less people at Ross interested in investment banking. I have also heard that they generally spend a full week in NYC and then come to NYC for a handful of Thursday/Fridays for interviews. If you're interested in investment management or private wealth management (which I think are very different things), it will be a similarly unstructured process. You'll have to network a lot and travel some, but you also have the advantage of being one of the few people actually trying to do that.
Conclusion: just because a lot of students go into finance does not mean you should necessarily go to a finance school as you need to look at the subset of finance. Investment banking is dominant at many schools and that is not relevant if you don't want to do banking.