Do you like Irish culture? There are some really good places to have the traditional Irish Breakfast (trust me, you won't need to eat for the rest of the day after one of those!) in Yonkers and New Rochelle.
Instead of being a tourist, I'd suggest you be a flaneur. If there's something you've always wanted to do, do it. But I wouldn't try to cram a lifetime's worth of memories in a few days.
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