Nick--
Matt is dead on with Oyster Bay. It's tight and has some really interesting (and tough) holes, despite it's lack of length (6,400). And, hey, if we're drinking muni juice, how about the Red course out at Eisenhower. That's the new venue for the LI Champions Tour event every year now (as well as the site of the 1926 PGA) - a old Emmet design that's may not be the toughest test but is real fun. And one more (I think Matt might have mentioned it) is Harbor Links in Port Washington - I think Matt just called it the Hurdzan Harbor. It's a memorable tract, really unique, almost-desert feel to it.
As for the suggestions of Timber Point and Lido, I think both of those links-style, on-the-water courses are great, too. Lido isn't C.B. Macdonald's "The Lido" of the turn of the century (that defunct site is across the street), but it's a interesting RTJ layout on Reynolds Channel. And Timber Point has some really great holes, a lot of them left over from the original Alison design - make sure you play the Blue-White combo and leave out the Red nine (it's 27 holes). I think both courses have previous threads about their history, with are both completely fascinating.
Long Island has a ton of great public courses, and, although Spring Lake is alright, there's a ton of better options. Enjoy.