There is an old town that lives at the end of Long Island, only 118 miles from Manhattan. In recent times it has become a summer destination for NYC to escape during the summer, and with it brings tremendous change to the town. There are more hotels, fancy restaurants, and a vibe that contradicts Montauk's past.
I grew up in Suffolk County Long Island, and have been going out there since I was a kid. It was a place where you're not defined by the tag on the back of your shirt, but the stare in your eyes or the smile/frown you owned based on good times and bad. T-shirts, fishers, surfing, and simplicity at one of the greatest beaches in the world.
The old Montauk still exists and is clear and more present in the off season months. This month I camped at Hither Hills State Park just west of Main Street. For $25 a night you can enjoy everything Montauk has to offer.
Bring your tent, fishing rod, some bucktails for the stripers, and be ready to go fishing at a moment's notice. There are many places to fish out in Montauk. Light House, False Bar, Hither Hills, Bluffs, and much more. If you're visiting Montauk for the first time, head to Paulie's Tackle for all the local fishing tips, good conversation, and some more bucktails.
I recommend heading out 45 minutes before sunrise, to hopefully catch some fish, and to see an incredible sunrise on the horizon of the Atlantic Ocean. Walking out in your waders into the warm ocean, and casting off while the waves crash on the shore, makes you quickly realize Montauk's draw. The fish are more likely to bite in the middle of the night or early morning. There was a storm that made it hard for me to fish at night, but as soon as it passed, I headed out at 4 am in a deep fog and a bit of rain to get the last cast in before I headed out. You can't see anything in front of you, but you start to make out shapes. You realize the darker it gets in front of you, and the larger the wave is. The ocean is extremely powerful and you feel humbled to stand in it up to your knees, cast into its darkness in hopes of catching a fish.