It's tricky but you can get on the 59th Street Bridge and avoid the tolls. Now if you want to go uptown from the bridge, you should take the upper level. If you want to go downtown, take the lower level.

This is what we do when returning from my inlaws. We take the LIE to the last exit before the Midtown Tunnel which is Van Dam Street. Turn right on Van Dam. Take it to the end which is Queens Blvd. You will see elevated subway above you. Make wide left onto Queens Blvd so you are underneath the elevated subway. Follow the signs (and stay in the left lane) until it takes you to the lower level of the bridge. THe lower level will put you on Second Avenue which heads downtown.

For the upper level, at the same intersection with Queens Blvd, turn at left arrow onto Jackson Avenue. Drive 1/2 mile and look for the signs which will guide you to the upper level. The upper level puts you on 3rd Avenue which goes uptown.