Does it have to be by Amtrak?
If not, here are my favorites:
1. LIRR Montauk Line to Southampton or Amagansett. Hang out in the quaint villages, visit the beach, have a nice lunch in the village etc.
2. LIRR Port Jeff Line to Port Jefferson, walk down to the harbor (about a mile downhill), enjoy the parks and shopping in quaint village stores at Port Jeff Harbor, then either trudge up the hill back to Port Jeff Station to take LIRR back, or better still take the Port Jeff - Bridgeport Ferry which runs frequently, to Bridgeport and then take either an Amtrak Regional back to Penn Station or a Metro North Express back to Grand Central and then subway to Penn Station.
3. LIRR Montauk/Speonk/Patchogue train to Oakdale or Sayville and then ferry to Fire Island. Spend the day on the beach and head back via Ferry and LIRR to NYP.
4. NJT North Jersey Coast Line to Point Pleasant Beach. Hang out on the Boardwalk or explore Point Pleasant Beach downtown. head back via NJT to NYP. Alternatively you could explore the village of Manasquan, the station immediately preceding Point Pleasant Beach, or even Belmar the station preceding Manasquan.
5. Amtrak Boston Regional to Mystic. I have heard good things about it, but never done it myself.
6. Amtrak Adirondack to Saratoga Springs and then possibly S&NC Dome cars to North Creek and back. AlanB is an expert at that one. I actually did it by driving to Saratoga and then taking S&NC.
7. On the Hudson Line I love the Village of Cold Spring. but you have to take Metro North from Grand Central for that one since Amtrak does not stop there. Fantastic views of Storm King Mountain from the waterfront, which is very well preserved in its old quaint state.
8. Amtrak Empire Service or Metro North Hudson Line (ex Grand Central) to Poughkeepsie, and then go for a walk across the Hudson on the old restored New Haven Railroad Bridge across the Hudson. Spectacular views specially during Fall Color season, but even otherwise. Specially on a clear day you can see the Catskill Mountains to the north.
9. NJT NEC Line or Amtrak to Trenton, and then RiverLINE DLRT to one of the various quaint little Delaware Valley towns that it serves. My favorites are Bordentown NJ and even more so Burlington NJ. Explore the town, the riverfront and have lunch at a riverfront restaurant. In Bordentown explore the first commercial railroad track segment of the old Camden and Amboy. From Bordentown all the way to Pennsauken the RiverLINE follows the right of way of the old Camden and Amboy.
10. NJT Midtown Direct to Millburn, Summit, Chatham or Madison. Hang out in the parks and have lunch at one of the many excellent eateries. The South Mountain Reservation Park is a short walk from Millburn station. You can also take in a play at the Papermill Playhhouse which is on the way to the South Mountain Reservation Park. This is deep in my (and Shanghai's) neck of the woods!
TAFN (That's All For Now)