If you're looking for a meeting place or a good stop around ½ or halfway between Lindenhurst and Long Island City, you can try Mineola, NY, which is about half an hour west of Lindenhurst, or about half an hour east of Long Island City.
About ⅔ or two thirds of the way, you can stop at North New Hyde Park, NY. This is about half an hour west of Lindenhurst, or about 19 minutes east of Long Island City.
About ¾ or three fourths of the way, you can stop at Queens, NY. This is almost an hour west of Lindenhurst, or about 14 minutes east of Long Island City.
If you drive straight through without stopping at all, the total distance is 39 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 54 minutes.
