NYU’s common data set indicates that they “consider” alumni relationship but it’s not an important criteria. Cost is probably more of an issue.
Here’s the website’s info on aid - average scholarship for students who get aid is 37K - but that average may be misleadingly high for a middle income family as it folds in larger grants for the 20% of students who qualify for Pell Grants (which => very low family income).
https://www.nyu.edu/admissions/undergraduate-admissions/aid-and-costs.html
You might want to run the EFC calculator - it could help you decide whether NYU is totally off the list.