Don’t know if you’re still in Flushing area JS but looking at Port Washington schedule it looks like not all the trains stop at Broadway, Murray Hill and Flushing Main Street. Some go right from Bayside to Woodside. Was surprised to see that as I took LIRR to work for many years from Murray Hill, Flushing.I would try flushing. Should have rooms between 150 - 225 and is walking distance to lirr. only 10 mins from LGA so most hotels have a free shuttle to the airport so you save 2 urbers. Some of the best chineese and korean food in the country is a plus.