I've done most of the drive/fly/train options. Nothing is really easy/fast/cheap, unfortunately.

EWR - YGK - you have to go through YYZ. Check your dates - the planes from YYZ-YGK are small and fills up quickly at end of term at Queen's, etc., driving prices up. If you have some flexibility of dates/times, that might help a bit. A cab from the airport to downtown is fairly cheap (approx. $12 CAD with tip) and quick.

YYZ --> downtown Kingston 2 hrs 45 min if no or light traffic on the 401. Add on a fair chunk at rush hour (took me 4 hours once at rush hour out of Toronto).

YOW --> downtown Kingston is about 1 hr 50 min taking Prince of Wales to the 416. The closest major airport to Kingston. You can take a city bus to the train station relatively easily if you prefer not to rent a car.

SYR - border crossing is usually fairly quick. Make certain your rental car company knows you're heading into Canada. The drive is about 2 hrs 30 min.

YUL --> downtown Kingston is about 3 hours. Some rush hour going in and out of Montreal (and the stop lights when the expressway ends just before Montreal), but the airport is on the west side of the city, so less of an issue than YYZ. The best plane - train connection is via YUL (if you prefer not to rent a car), as there is fairly easy access to the Via Rail station near the airport, and the station in Kingston is convenient.