Outside Manhattan is good, as long as there's a metro line close by the hotel. Last time I was in NY we stayed at The Box House in Brooklyn, parking was on the street, and the hotel was not far from metro line (just crossing a bridge) by foot.
We are 2 families, 2 adults each, so the price will be by room/family. We are aiming to not go over 180USD, and we just want a hotel with good reviews. Of course, if we could get a reasonable parking cost for 4 days elsewhere, near the hotel, that will good too. We will not use the car at all during these 4 days.