Downtown JC sometimes gets called the "sixth borough," but honestly that's not accurate. It's the third borough. Jersey City feels more like Manhattan and Brooklyn than the Bronx, Queens, or Staten Island do, and it's certainly closer to the heart of the city than those boroughs.

I love it here, so I might as well start with the downsides:

• If you're moving from Florida and haven't lived for protracted periods in the Northeast or Midwest, the climate is going to be an adjustment for sure. I know that "goes without saying," but my partner from Memphis still struggles to adjust 15+ years since moving up North.
• It seems like politics is part of the reason you're considering a move, so it's worth saying that politics in New Jersey generally and Jersey City in particular can be head-thumpingly frustrating if you're a motiated progressive who cares about multiple issues. Democrats rule unopposed here, and use their full-throated support of LGBTQIA+ rights, women's rights, and Black Lives Matter (on paper at least) to deflect from deeply corrupt commitments to machine-style politics you might have thought had died out some time after the Gilded Age. Shit like our county executive promising to end ICE detention centers in our county, and then going back on his word essentially in the dead of night for no better reason than wanting ICE cash. Our Mayor and his hand-picked slate of City Council people making land use decisions on behalf of developers that don't seem to benefit the community, and then magically getting millions of dollars of in-kind contributions like mansions on the coast from those same developers. Don't even get me started on the long-running scheme to raze a sensitive bird habitat in Jersey City's largest park so that a billionaire buddy of the governor can turn it into golf holes for the ultra-wealthy (see: Caven Point, Paul Fireman, for more information). Point being, if you want to live somewhere to experience the idea that liberal Democrats can run communities that are not only inclusive, but also equitable and well-governed, this is not the place for that, our leaders are too addicted to developer money. Maybe coming from Florida this sounds like a relatively good problem to have, you'd know better.
• There is a very real social stigma against New Jersey, and not just coming from New Yorkers. Being relatively local, it's actually been pretty easy to get my NYC friends to realize "holy shit, Jersey City is closer and more convenient and more fun than most of what's 'real' New York." But I've been on the other side of the fucking country and had folks say something along the lines of "where ya from?" "New Jersey!" "I'm sorry." Again, being from Florida you may already be used to worse.
• Flooding is a serious concern. If you're not buying property I wouldn't worry too much, but if you're looking at renting a garden level place, make sure it's flood-proofed. And don't necessarily take a landlord's word for it.
• Crime is mostly non-violent, but hoo boy the porch pirates and drunk drivers can make life difficult. We get roughly half the packages we order, due to either package theft or delivery service incompetence. We have to street park our vehicle like most Jersey Citiots, and at this point we don't bother getting dings and dents repaired because there are just going to be more later.
• Speaking of cars, parking sucks. I'm torn on whether or not to recommend having a car, because you've mentioned wanting access to nature, and a car is the best way to ensure that (ironically enough). But since this is the "negatives," having to move your car for street-cleaning in the middle of the workday multiple times per week is just not fun.
• You're not going to love paying taxes in Jersey City coming from Florida.

Alright, positives:

• In terms of being a "true city," yes, downtown JC is about as "true city" as they come. I have lived in Boston, Brooklyn, Manhattan, Seattle, and now downtown JC, and JC compares highly favorably. MOST of my friends who live in New York City proper do not enjoy the density or proximity to services or attractions that I enjoy in downtown JC. And I'm not even considering my friends who live in Queens, I mean like brownstone Brooklyn or northern Manhattan.
• The best views of the NYC skyline are over here, where you can see the whole thing because you're not part of it.
• You do not need a car. You might want one, and unlike in Manhattan it is possible to have one, but you do not need one. We have a car, but I do not drive within the metro area, the car is only for longer, regional trips.
• There is plenty to do here. The restaurant scene is excellent, and I honestly can't think of a restaurant that doesn't have compelling vegan options. JC is small enough that it can really feel like a community, and there are events all the time. There are some performance spaces here, most notably White Eagle Hall that frequently hosts excellent acts, if not acts that would sell out stadiums. We basically only cross the Hudson to see friends or theater, maybe the occasional museum. For nightlife, the quality is higher and the prices are lower on this bank of the Hudson.
• And when you do want to get into Lower or Midtown Manhattan or even northwest Brooklyn, JC's a more convenient starting place than most of NYC.
• Your only problem being gay here will be people falling all over themselves to affirm your identity. One of my gay friends from rural Texas finds it mildly creepy how aggressively supportive everybody is regarding his sexuality.
• There is indeed decent nature not too awfully far away! We usually drive a couple hours' north to the Catskills for camping, hiking, etc., but you can actually take a train to a lot of these locations. . . though you'd almost certainly need a car on the other end unless you're extreme hikers. Also nice, a lot of these little rural towns just upstate along the Hudson are themselves highly progressive. Expect New York prices, unfortunately, but the nature is, in my opinion, top-notch. I could have more recommendations here, I camp a lot.
• Not quite "nature" as I envision it, but the parks here are beautiful and well-maintained. Lots of trees, flowers, frequent farmers' markets. And then Liberty State Park is a goddamned treasure, if we're willing to fight to keep it. If you're craving a closer-to-home nature experience, you could totally bring a book or a picnic to a JC park and get your hit of trees, grass, flowers, etc. Depending on the park, like Liberty or Lincoln, you could even enjoy some silence (not likely in Hamilton or Van Vorst).

Any other particular areas of concern?