You might give the Basilica of the Sacred Heart a try. It’s beautiful and they have both the Extraordinary and Ordinary forms there, though I’ve only attended there for the former.
Edit: while in the area you might also want to visit the convent of the Sisters of St. Francis, where the tomb (or whatever the proper term is) of St. Marianne Cope is. I don’t know what the liturgy is like there though (my experience with the sisters while mostly positive does not give me great confidence that they would have a very good liturgy. I attended the Transitus of St. Francis there a few times and liked it, though my memory is vague on it and I wouldn’t know what the Transitus is supposed to be like). Actually I just Googled it and it looks like since I was in the area they’ve made the place a real shrine and museum:
blessedmariannecope.org/shrine_museum.html
If you will be in Syracuse the city I would suggest the Basilica as well, though I too, was only at the EF there, when the dearly departed monsignor was still there. Otherwise I attended the NO at the Cathedral of the Immaculate Conception. (On Sundays you can park for free, but be careful on weekday HDO’s you can get a ticket). I preferred the Sunday morning masses as the Sat mass had the folk music group sing, and the Sunday evening Mass was the fullest mass. The homilies could be a little weird and the music a little showy*, but otherwise it was generally a restful/peaceful mass experience.
Syracuse (the city) is quite small, so it is no problem to drive to either of those churches if you live in the city limits or in the first ring suburbs like Liverpool, East Syracuse, Even Fayetteville (It seems a long way away, but we would go over there to eat after Mass downtown sometimes). Bishop Cunningham was installed while I was there, and he is a pretty solid bishop, but he has a lot of obstacles is his way, and now is the apostolic administrator of the Rochester Diocese which would be a daunting task for anyone.
I don’t know where you will be staying, but can I recommend you stay away from the immediate South West side of the city.
Let us know if you need to know anything else. I spent my first 2 years there shopping over in Fayetteville, and only my last year there found the Target over on the West side. (Though Fayetteville/Erie Blvd. remained our primary shopping area).
*By showy, I mean that the cantors often had show tune type solos during mass or right before that would provoke applause from the congregation. There was one cantor in particular that we called opera guy, and while there is really nothing wrong with opera, him singing Lord of the Dance came off as a little much.
