If you're looking for a meeting place or a good stop around ½ or halfway between Syosset and Weehawken, you can try Fresh Meadows, NY, which is about half an hour southwest of Syosset, or about half an hour east of Weehawken.
About ¼ or a fourth of the way, you can stop at Westbury, NY. This is about 15 minutes southwest of Syosset.
About ⅓ or a third of the way, you can stop at Mineola, NY. This is about 18 minutes southwest of Syosset.
About ⅔ or two thirds of the way, you can stop at Walden Terrace, NY. This is about half an hour west of Syosset, or about half an hour east of Weehawken.
About ¾ or three fourths of the way, you can stop at Linden Hill, NY. This is almost an hour west of Syosset, or about 15 minutes southeast of Weehawken.
If you drive straight through without stopping at all, the total distance is 32 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 59 minutes.