@Joshua Goldberg if you're willing to drive an hour of Hudson county there's basically any type/class of property you could possibly want. Sort of depends on your desire to be within proximity of public transit to, say, NYC and your tolerance for living/investing in areas that may be seen as less desirable. Some general thoughts:
Hudson County is very competitive right now, but there are still some "marginal" areas that offer investment opportunities. Greenville, in Jersey City, has a pretty negative reputation (some areas are quite unsafe), and is not particularly well situated to public transit, but certainly offers buy and hold opportunities currently in your budget. Sporadically, you may also be able find deals in Union City, North Bergen, and West New York, and other ares of JC, but those areas are quite competitive.
Essex County (which includes Newark) is also quite competitive, but, if you're willing to invest in less desirable areas like Newark (not the Ironbound, though, which is going to be too expensive for your budget), East Orange, or Orange, there are lots of opportunities for pretty solid cash flow. The problem in those areas (similar to Greenville) is stabilizing the property: so finding quality tenants that will pay rent on time, in an area that is at least safe enough where you'd feel OK doing renovation work, collecting rent, etc. There are deals you can probably find on the MLS right now in East Orange and Orange below $400k that will yield some pretty good cash flow.
Passaic (in Passaic county) can also yield some deals, though I haven't personally invested in the area.
All of the above areas are pretty block-by-block, though, so if you're not familiar, I'd recommend spending a few weekends driving around and getting sense of the areas. All of those cities have "good" and "bad" areas (and are priced accordingly), so it may be in your best interest to be a little bit picky about exactly where you want to invest.
I'm not as familiar with further west and/or south--if you drive basically an hour west of Hudson county you'll be in essentially farm country, hah. I've invested in Hudson, Bergen, and Essex counties, primarily for buy-and-hold properties, and have done quite well.
Best of luck!