Yannick,
I played down there at Bethpage on 6/17, and it was a great experience. The course is very well-maintained, and there are some holes out there where you feel like you are in heaven. I will say that some of them appear more new (Rees) than old (Tillie), as it seems some of the quirk and old-time design has been covered over with huge sweeping waste bunkers and mounding. Despite this fact, it is apparently much better than before, and the course was not going to be a US Open test with the original bunkering.
As for tee times, the only way to adaquately do it on a weekend is to find a friend with a NY state drivers license to play with. If you do that, you have to get his name and license # in their tee time system, and once that is done (takes a day pretty much), you/he can call 7 days in advance of the day you want to play starting at 7pm, using the # to try for a time on the automated system. For a weekday, I imagine less people would be calling, and it would be slightly easier to get a time. The catch is that if you make the "NY resident" time, he has to play with you I think, as they check his/your ID upon check-in. If this is not possible, then your best bet is to line up in your car, before midnight gets you the first spot in line for a weekday, and I imagine around 8-9pm would get you near the top for a weekend time. The only annoying thing about that process is if you arrive late, you will not get an open time until late in the day, making the wait even longer.
Hope that helped...