If you mean nature in general, I've never been, but I hear City Park is gorgeous for walks, and it's bigger than NYC Central Park. I can't speak to what crime is like there, but it sounds fine if you do it during the day and stick to main paths. Of course there's bayou fan boat tours as well, which I also haven't done but it's on the list.
If you mean just being outside, it's been mentioned, but I'd highly recommend taking the trolley through the historic Garden District. The trolley itself is fun, it's turn of the 20th century real historic street cars, that slowly take you through the main areas, as it goes right through the Quarter and through neighbouring Garden District. It's beautiful old plantation style houses with large southern trees, just get off anywhere nice to walk through the neighborhood and check it out. When you get tired, catch the next trolley.
And if it's hot and you're getting "parched", similar to Vegas, you can walk around drinking, it just has to be in an unmarked "to-go" cup (like college party style cups). Pretty sure I even took one on the trolley. What blew my mind is you can even walk into establishments with one (at least the ones I went to).
Last thing, obviously it's great food there. It sounds cliche, but locals simply advise you to "follow your nose", as there's so much good food everywhere that you really can't go wrong wherever you are.
EDIT: I find this channel gives great advice on what to do in NOLA, check it out if you want:
https://youtu.be/kAiLpTt-ydw?si=qK85EakuD_rDSRRJ