I have only run it once, and it was a crazy weather day (2015) with 20-25 mph winds, so my experience may not be representative of others' experiences.
As noted, the Verrazano is all uphill that first mile. You'll remind yourself to not push it up (and then down) it, but you'll probably do it anyway.
Once you come off of the bridge it is a straight and mostly flat shot for a really long way - several miles. In my opinion, the crowds on 4th Avenue were the best crowds I've experienced in my 4 marathons (Boston and Chicago twice were the other three).
At some point after 4th Avenue you will enter into an Orthodox Jewish neighborhood. The residents don't acknowledge you at all and it is eerily quiet, especially after coming away from huge and vibrant crowds. This is a pretty cool thing and it's own way, so try to appreciate it.
Did you go over a small bridge before getting to the Queensboro - that one isn't a big deal. The Queenaboro is a big hill. Sure, it's early enough that it isn't awful, but it will slow your mile pace down down by :20-:30.
You come off of the bridge and wrap around a little bit before you hit First Avenue, which gets the most hype as Supplying great crowd support. I don't think it beats Fourth Avenue, but it is still great, especially after the silence on the bridge. Most of the first Manhattan stretch is flat to gradually downhill.
Then you curl through the Bronx. It is crap - no crowds because you are mostly in an industrial area. It's only a short stretch though. The little bridge out of the Bronx isn't bad, but it is late enough that you might feel it a little.
You eventually make your way to 5th Avenue. The slight uphill nature of this part of the course along with it being at the point in the race where you might really start struggling anyway makin it deceptively tough. The race has really begun now.
You enter the park and it is all rollers until you exit the park. Not a ton of fun if you don't have a lot of experience running hills, and even then it isn't much fun because they come so late in the race.
You exit the park and run along the southern border of the park - I was in no man's land when I got here and had a headwind - it is a half mile or less and I felt like it went on forever.
The. You turn into the park for what should be a short finish. I was riding the struggle bus at that point and it felt like it took forever. The crowds are thinner and more subdued here than you would expect. A tough way to finish.
Then exiting the finish area is a nightmare.
A really great experience overall, and you'll love it, especially if you are ready mentally for the challenging parts.
Have fun.