There is sooo much to do in NYC that I hardly know where to start.
If you're into art, you must visit the Metropolitan Museum of Art. There is also the Frick Collection - this is a relatively small collection that can be easily viewed in a morning.
Visit the Museum of Natural History if you can... this is my favorite, but then, I'm a science geek
Weather in mid-June can be pretty variable... it's often hot and humid, but it can still get a little chilly at night. You may want a sweater and/or light jacket for the evenings, but otherwise, you should be fine with lighter clothes. Check the weather forecast a couple of days before you go.
Enjoy!
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