1. every census that your grandfather will appear in should have a column asking either "How long has this person been in the US" or "What year did they arrive in the US". Many states (especially NY) did their own censuses in between federal census years and also asked this question. From the answers, you should be able to get a good approximation of the year that your grandfather arrived.
2. if any of your foreign-born family members naturalized, or, if any of the foreign-born males registered for the WWI draft, those documents will list the town from which your family came.
3. if you know the name of the cousin that family lore says your grandfather came with, so much the better"
Not necessarily true. I have seen censuses and WW I draft notices which don't give this information. Just because you have seen the year of arrival on a couple censuses, that doesn't mean they all have them.
And if family lore says somebody came with somebody, that isn't necessarily true either. My mother, for example, mixed lots of stuff up. My grandfather was born in Missouri or Wisconsin or somewhere, for example.
Sally Bruckheimer, Princeton, NJ <sallybruc@...>