From my place in the 20's on 2nd, it is clear that the tunnel is the quickest route to/from LGA. Unfortunately, once in a while the combination of me forgetting to tell the driver when I get in the car, them trying to take advantage, and me not paying a attention ends up with me going toward the bridge. The few occurrences where this has happened, by the time I realize what's going on, turning back toward the tunnel would end up costing even more. In cases like this, I just screw them on the tip. And I feel fine about that.
Like you, exmontrealer, I've just gotten into the habit of telling them to take the tunnel. Sometimes they put up a bit of a fight but they always end up doing it.
A bit OT - one time a car service I use (relatively high end Town Car - about $100 NYC - LGA) took all sorts of back roads from LGA to my place. I had actually fallen asleep and when I woke up we were in the middle of Queens and ended up going over the 59th St. Bridge. When I started yelling at the guy he said that it was quicker. I think he was doing this to avoid paying the Midtown Tunnel toll (since the service was prepaid including tolls/tip). Took about 50% longer, just another scam to be aware of.