OK, to sum up, you can get between the following areas for free as follows:
Between Manhattan &The Bronx (Westchester/Connecticut):
The Willis Avenue, 3rd Ave, Madison Ave (138th St), 145 St, Macams Dam, Alexander Hamilton (179th St), Washington (181st Street), Univesity Heights (207th St), & Broadway Bridges or Henry Hudson Bridge (northbound only)
Between Mahattan & Brooklyn/Queens (Long Island):
Queensboro (59th St), Williamsburgh, Mahattan & Brooklyn Bridges
Between Manhattan/NY East of Hudson & New Jersey/NY West of Hudson:
Westbound (toward NJ): Lincoln Tunnel, Holland Tunnel, George Washintgon Bridge, Tappan Zee Bridge, Bear Mountain Bridge, Newburgh-Beacon Bridge, Rip Van Winkle Bridge
Eastbound (toward NY): No bridges below Albany. In Albany, either the Dunns Memorial Bridge or Route 90 Bridge.