Red,
I love to just get in the car and drive as well. On LI, I would drive down to Ocean Parkway on the South Shore, which runs all along Jones Beach and Robert Moses State Park. At night it was particularly calming.
My kids (now 26 and 22) often tell me that some of their best memories are of our many road trips up and down the East Coast, from Montreal to Florida and everywhere in between, playing Wilie Nelson tapes with a cooler full of snacks, sandwiches and frozen juice packs in the car. They both enjoy road trips now as well.
As far as the price of gas, I drive a Mini, so luckily I can still indulge in my drives.