David's Bridal is probably one of the best options for gowns under $1,000. Would you consider buying online? If so, you could check out stores like ASOS (have some bridal options), BHLDN, Modcloth (some bridal options), and Lulus (have a few white dresses that can be bridal).
Alternatively, you could look at bridesmaids dresses that come in white. Many of them look very bridal and would be perfect
Sooo I'm not 100% sure, but I think when I went to Rana Bridal in Englewood there was a dress I tried on that was slightly under 1k. I may be wrong though. I would call and double check. I do remember though if you buy the dress the day of your appointment you get 10% off.
Also, have you looked at Etsy? Some of their dresses look adorable and you can get them for a few hundred. Also Nordstrom has a bridal suite. I know there's one at Garden State Plaza.