Is Stuyvesant Town in New York City walkable? Can I walk to everything or do I need a car?

Stuyvesant Town is more of a massive apartment complex than a neighborhood. You can walk the entire thing in 10 minutes. So, yes, it's very walkable and it's pretty central to other neighborhoods that will have everything you need. You can get as far as The Bowery / Nolita in under 10 minutes by foot so you definitely won't need a car.