Jersey city is great and 3.5k budget is reasonable. You can find a spacious one bedroom in that range. Possibly 2 bed but smaller common areas. Anyways, jersey city and Hoboken are an easy commute to the city and safe. Jersey city is pretty big but if you stay downtown or near the water, you’ll find it’s a similar vibe to Brooklyn. The food is great but the night life is definitely much slower paced here. Nothing a quick path into the city can’t fix though. I’d recommend spending some time in the area before making the decision. I’ve never lived in Brooklyn but I love it there. I’d choose jc or Hoboken personally.