This is probably a longer answer than you're looking for, but as someone who has cumulatively spent whole days of my life sitting in the little coffee shop in the ITH terminal waiting for fog to clear, here is my take:

I think the primary consideration should be whether you will need or want a car. If you want a car, I'd probably compare the sum of car rental and flight costs for ROC, SYR, ELM, and BGM and make my decision based on that. SYR, ELM, and BGM are each within an hour's drive; ROC is a little further but has more direct flight options.

If you like scenic drives, I'd second Letitride in also considering SWF. It's a beautiful 3 hours of highway driving straight through the Catskills to Ithaca.

If you're not driving and flying into ITH is ruled out, you'll likely arrive by bus from NYC. Unfortunately, scheduled passenger train service to Ithaca was discontinued decades ago. Coach USA/Shortline offers single-coach service from Port Authority approximately every two hours via Binghamton. Total trip duration is about five hours. Fare is about $120 r/t, IIRC - though you could save by buying one of Coach USA's codeshare services with Megabus into Binghamton and buying a second ticket for the last leg into Ithaca. Yes, Megabus has codeshares...

The other option, and probably the one most Flyertalkers would prefer, is the Campus-to-Campus bus service offered by Cornell University. Their prices are higher than Shortline (up to $180 r/t), but the bus is comfortable (snacks, wifi, tray tables, 2-1 seating) and you must reserve tickets in advance online. They leave from the Cornell Club near Grand Central a few times per day. Despite anything you might read elsewhere, you don't need any Cornell affiliation to travel with them.

Obviously, you have to budget for travel time between the airport and the bus stop in Manhattan if you use either of these options.

There is also a company called Ithaca Airport Limo that still provides shared van service to SYR, though I recall their services being overpriced for what it was. I also once flew into BGM, took a taxi to the downtown bus terminal and then caught the end of one of the Shortline bus routes that originated at Port Authority for the last hour into Ithaca - but be forewarned that taxis are expensive in upstate NY and there is still no Uber/Lyft in the region.

OK, so that was a huge brain dump of my accumulated knowledge of Ithaca travel options. You might actually find more info about public transit options on a student forum site like College Confidential if so inclined. Hope this helps!