Yes, Lisa, probably in the areas I mentioned a car would be desired, unless you lived pretty close to the Railroad line I guess, with direct access into the city. I think the Bayside/Bay Terrace area does have a number of apartments for rent. Little Neck and Douglaston are a bit more tricky. Not as many apartments, but a number of people tend to rent out houses, and co-ops remain pretty reasonable. All 3 have pretty decent size Jewish communities, and singles as well as families. Good luck in whatever your choice.
P.S. I have always liked visiting Forrest Hills, though I never looked into living there.