Another resource that I use is Wikipedia. Of course, you are at the mercy of whoever edits the page.

Currently for LGA:

* AA mainline: Atlanta, Aruba, Bermuda,[114]Charlotte, Chicago–O'Hare, Dallas/Fort Worth, Denver, Houston–Intercontinental,[115]Miami, Nashville, Pittsburgh, Raleigh/Durham, St. Louis, Washington–National, West Palm Beach
Seasonal:Bozeman,[116]Columbus–Glenn, Eagle/Vail, Glacier Park/Kalispell,[117]Jackson Hole, Montrose, Nassau


* AA Eagle: Akron/Canton, Atlanta, Charlottesville (VA), Chicago–O'Hare, Cincinnati, Cleveland, Columbia (SC), Columbus–Glenn, Dayton, Detroit, Fayetteville/Bentonville, Greensboro,[119]Houston–Intercontinental, Indianapolis, Kansas City,[117]Knoxville, Louisville, Memphis,[120]Minneapolis/St. Paul, Montréal–Trudeau, Nashville, Norfolk, Oklahoma City,[115]Omaha,[115]Pittsburgh, Raleigh/Durham, Richmond, Roanoke, St. Louis, Toronto–Pearson, Washington–National, Wilmington (NC)
Seasonal:Destin/Fort Walton Beach, Hilton Head, Key West, Martha's Vineyard (ends June 17, 2022),[121]Myrtle Beach (ends June 2, 2022),[121]Nantucket (ends June 17, 2022),[121]Nassau, Rapid City,[117]South Bend, West Palm Beach

This is usually a good starting point for me, or even the airport website itself; however the LGA website doesn't seem to list destinations, not like AUS does at least.