Hi Lh06465n thanks for your question. I see that you didn't receive many answers and I know the reason why. As real estate agents, we cannot comment on the safety of any particular neighborhood or make any recommendations as to what areas are "good areas". There are laws that protect against discrimination to any party and so we have to be very careful as to how we answer questions. This is to make sure that you are not steered towards any particular neighborhood.
With that said, both Hoboken and Jersey City offer excellent options for a quick commute to NYC.
In downtown Jersey City and Hoboken, the prices are higher than in the surrounding neighborhoods. This is primarily because these two area's have the PATH train which runs direct into Manhattan. Other area's such as Jersey City Heights, Union City and Weehawken, stretch your dollar more in terms of buying power, but the residents of these area's rely on bus transportation to the Port Authority in Manhattan which is very reliable and is also a short commute depending on how far the stops are to the Lincoln Tunnel.
Personally I've lived in Union City, West New York, Jersey City Heights and Hoboken, and all offer wonderful things individually.
So you will want to explore all, and take into consideration your buying power. Make sure that you get pre-qualified first, then make a list of the things you'll want in a home. Price will most likely dictate where you will buy as it is difficult to find a home in Hoboken and downtown Jersey City larger than 700sq ft for less than say $300K in these areas.
Hope this helps!!