I live on LI myself, and went to Birch Hill a couple of months ago to see In Flames, who chose not to stop in NY at all. Driving there from LI is fairly simple. I don't know where you are on LI, but I'm on south shore and wouldn't suggest taking the GW brdge - this place is south of Staten Island. Take Verrazano and Outerbridge Crossing (not Goethals), and follow the directions to Rte. 9 South. Just stay on Rte. 9 until you pass Texas Rd. light (you really can't miss it), and then watch carefully for the Birch Hill billboard on your right side, there will be a sharp turn right before the billboard.
One thing to watch out for - as you cross the Outerbridge, make sure to check what the billboard says. On some days of the week, the bridge is closing at midnight, so you may end up taking the Goethals back.
Now that you have the directions, I actually don't recommend going there, unless you can't make the NY gig on Saturday. First of all, traffic is killer. Make sure to leave really early, if you want to cross Verrazano without sitting on the Belt for an hour just to get on the bridge. Second thing is the tolls ($7 for Verrazano and $6 for Outerbridge/Goethals), which is almost as much as the price of the ticket .
And filnally - Birch Hill is a terrible venue! I'll give them a credit for good sound, though. But - the stage is only about a foot high, so unless you are all the way up front, you will only see the guitar players from about chest up. I was on a second level by the soundboard and even with the unobstructed view, I could not see shit! Another thing is, it was incredibly hot there when In Flames were playing, we are talking over 90 degrees. I nearly passed out of heat exhaustion towards the end of the show. Don't know if this has improved since then.
And - almost forgot! There's a long line to get into the club, so make sure to arrive at least half hour before the show starts.
-GK