Old Salt (Syracuse) is roughly the center of the state which isn't a bad place to be because you're not too far from lots of things. The Adirondack Mountains to the north, the Catskill Mountains to the south east, the fabulous gorges of Ithaca and Watkins Glen to the south, the great gorge of the Genessee River and the Niagara Escarpment to the West.
My best advice is to contact and consider joining the Onondaga Chapter of the Adirondack Mountain Club - https://www.adk-on.org. Nearly all chapters have organized outings and many of the members are runners as well as hikers, etc. Good news too, the chapters are resuming hikes and other activities this June after being on hiatus due to the pandemic for the better part of a year.
Good luck to you Rauletto.