Since your flight is at 5:30, you'll need to leave for the airport no later than 1:30. You really do need to be at JFK 3 hours ahead of time just be safe if you don't have pre-check. I think 20 to 30 minutes in the security line at that time of day is pretty accurate. I've flow out of Terminal 4 a few times in the past few months, and the afternoon lines can be long. But this being on Sunday is completely different. There won't be nearly the traffic that you'd see on a regular weekday. Still, I think you'll be fine with public transportation, which will take a bit over an hour. You switch to the Airtrain at the Howard Beach subway stop on the A train.

You probably won't have time to do both the Statue of Liberty and 9/11 Memorial (since both take multiple hours), so you'll likely have to prioritize. What I'd suggest is that you get up very early and take the Staten Island Ferry to and from to get a look at the statue in the morning sun. It's a nice ride, but the round-trip will take about an hour (less if you are able to get back on the same ferry to return, and it's free (or even better do it the night you arrive ... the ferry ride is great after dark, and the ferry itself runs 24 hours ... though not as frequently after commuting hours). The pedestal at the Statue of Liberty no longer holds a museum; a separate new museum opens in about a month, and all the artifacts have already been removed. I'm not sure what's going to be installed inside the pedestal (it may just become the waiting area for those climbing to the crown). But if you want to try to do both, then still get "pedestal access" (which will get you into the new museum) and do the Statue first thing, but the first ferry isn't until 9:30, so I think you see the issue.

A better alternative might be to visit the Museum of Jewish Heritage to see the temporary exhibit on Auschwitz, which will display many artifacts for the first time ever in the US. It might add up to a very somber day, but it's a wonderful museum, and I think it would be time well spent. Even if you don't want to visit the exhibition, there's a railway car displayed outside the museum right now. If you want to see this exhibit, you'll need to buy advance tickets; it's going to be very busy.

But there's a lot of other stuff to see in Lower Manhattan, so you won't have any trouble at all filling up several hours.

Doug: I paid $60 to JFK from my house about a month ago. I've never paid anything close to $70 to JFK! I took Carmel. And I never pay tolls and I tip well. It depends on where you live in Manhattan.
I probably had a Carmel coupon but those are very, very easy to find.

I fly out if JFK for inernational flights and I get there 2 hours ahead of takeoff time. I've never had a problem. Never been there three hours early.

Thanks again for all of the tips. The Auschwitz exhibit sounds like something we would like to see so I'm going to look into that....you are all correct, we need to prioritize :-) !