Grinnell is a very good school. What’s the difference in money? If it’s only a few thousand, it might not be worth the difference to your family. If it’s substantial, Grinnell is hard to say no to. I know of a student there who loves it. (Perhaps @porcupine98 could weigh in?)
In short, you will have opportunities to do research at LACs and you won’t be competing with grad students for them. In your position, I’d start by getting rid of the one you like the least. Then seriously consider the kind of environment you want. The beauty of LACs is that you will get to know a lot of your fellow students and professors quickly. Professors will know you on a first-name basis. That is less likely to happen at a research U. At LACs, your classes will be small from the start. My D’s two largest classes had 60 and 25 students. A class with nearly a thousand kids will not be unheard of at UCLA. Not sure about Northeastern.
Will you like the co-op system at NE? It’s not for everyone, and your degree typically takes five years. It’s very urban, completely different from the LACs, with no defined campus. I know several kids who are having a good experience there, but they do spend a lot of their time going out in the city. It’s going to be different from the traditional campus experience if that matters to you.
Both Bates and Grinnell are going to give you the types of opportunities you are looking for. As far as vibe, my understanding is that Grinnell is perhaps a little more eclectic than Bates, but I suspect overall that a student on one campus would be happy on the other. As far as undergrad research, that’s something LACs are known for. I can’t vouch for Grinnell, though I expect it’s similar, but my D at Bates is doing research this summer. She’s a junior currently. Her friend is doing research at Brown this summer, and had two research positions last summer.
Biology and neuroscience are going to be good at all those schools (actually, I don’t know about neuro at Grinnell. Does it have a neuro major?) Bates has a neuro major and there are two hospitals close to campus. Bates and Grinnell have high rates of acceptance to grad and med school.
You will be fine as an international at all of those schools. They all have a good mix of students, especially Northeastern. I know the most about Bates, as my D’s best friends are originally from Tunisia and the Philippines. She has friends from Morocco and Kazakhstan. Her friend’s boyfriend is Vietnamese.
It might be helpful if you give us the total COA for all of your choices, or at least the two you are most interested in. Good decisions to make!