I used to live in Rockville Centre, so I know your predicament with the roads. On days I just wanted an unfettered ride without having to deal with cars, I'd ride over to Cedar Creek park in Wantagh and then just ride circles on the loop road going around the park. There's hardly anyone there most of the time, so you have a 1-way road all to yourself. Sometimes for variety I'd go onto the Wantagh Parkway bike path, but it's really hard to ride at a decent speed there what with the tons of cyclists and rollerbladers on that path on some days.
One ride I used to do quite a bit was to ride Sunrise Highway out to where it forks onto 27A, and ride that all the way down to the end of the babylon line, and follow montauk highway for a while till I was tired. The plus side was if I got hurt or had a mechanical problem which I couldn't fix (only once, but the added security is nice) I could just take the train home. There's a few nice county parks on the way where I'd stop and eat my sandwich, rest and then turn around.