If you are wanting to tie your own flies for your trip, I would suggest the following;
Egg paterns, San Juan worms and Crackle backs all work well at Montauk and are an easy tie. Depending on the water depth, I would also consider some wooly buggers in olive or black. Cracklebacks are great because you can fish them wet or dry. I prefer a size 14 in pumpkin orange.
Good luck on your trip,hope you catch a lot of fish!