And I almost didn't stay because of those reviews, but they generally repeat the same complaints:
1. It's really expensive & the rooms are small (true for the day rates, but overnight rates are often $300 for an "executive" room which is at least the size of a normal hotel room)
2. You have to use a self-check-in kiosk (true)
3. There's no microwave in the room (true; common complaint on TA which always amuses me because it's the roach-motel crowd that expects microwaves)
4. They charge for the pool during peak season (true after 11am, but free before that)
5. They don't give free upgrades or late check out (true)
6. There's no free breakfast (true)
7. The carpet is nasty (false -- we didn't notice any problems with the red carpet in the hallways during our stay, and the rooms themselves were not carpeted and were nicely decorated)
8. There's no trash can in the bedroom (true and totally bizarre, there's a "trash pad" placemat on the desk where they suggest you leave trash but no proper trash can other than a very small one in the bathroom...)

We went in knowing the above, though, and thought the TWA was the perfect hotel for the night before a JFK flight. We were able to walk indoors to the JetBlue counter, but you can also walk outdoors to the AirTrain to get to any other terminal in minutes. The hotel was fun and had museum-like installations at the ends of the hallways, the heated pool was great, and the airplane bar was fun. I haven't done the Hyatt yet but the TWA is a winner as long as you're prepared for the caveats listed above.