I am not sure how close to NYC you want to be. However, another answer I think is right in suggesting UVM. You might want to take a look at the CREAM program at UVM. I am pretty sure that UNH has a similar program. If I am remembering correctly this will include things like drawing blood and administering medications (cows apparently cannot swallow pills so if you need to give a cow a pill you get to put it inside them – probably already enough to explain why I was a math major instead).
All of UVM, UNH, and U.Mass Amherst are quite good for animal science. I think that with your great grades acceptance is very likely for all (I think that they are probably safeties for you), and merit aid is possible. I do not know your chances at the other schools as well but you appear to be a very competitive applicant at any university, even the most selective ones.
Wellesley College is an excellent school with an attractive campus. However, I do not think that it has animal sciences and I do not recall ever seeing large animals or a farm on campus (I took a couple of classes there many years ago as a cross-registered student from MIT).
I think that Cornell is a good choice for a reach. It is of course very strong in many fields including biology and animal science. The winters will be quite different from what you are used to but you should be able to get used to them and appropriate gear will be available in stores nearby.
I do wonder whether you should consider UC Davis in spite of its rather great distance from NYC.
This is a very good point to consider. It takes a lot of determination and time and effort to become a DVM. Reaching inside a cow, being bitten and stepped on and pooped on, and seeing beloved animals die are all part of the job (as is getting a rabies vaccination before you even start). I remember my daughter telling me about a day in the large animal drop in clinic when every patient died except a rat with pink eye. This included two beautiful horses that died of colic. The next day another horse came in with colic and it took them hours to save it. “Mental toll” I think is an accurate description.
It is relatively common for students to get their bachelor’s degree, work for a couple of years, and then decide whether or not they want to go back to university and get a DVM (or some other graduate degree).
These are worthwhile, but do not pay well.
There is a lot to think about here, but you have a lot of time. At the point that I graduated university (with a bachelor’s degree in mathematics) I still had no idea what I wanted to do with my life. This is quite normal and in general we all figure it out over time with the help of the experience that we get along the way.