There is so much to see. I'd suggest you visit their website to find what most interests you, and head to these spots first.
The strongest point of MET is not hispaintings collection but his historical representation of ancient buildings and rooms. If you are short of time spend it in the ground floor.
That depends on what speaks to you: painting, sculpture, period rooms, Central American pre-Colombian gold, etc. You should concentrate on one or two areas thst appeal. Then you will discover other things on the way. The Armenia exhibit is very interesting, at least to me. The Temple of Dendur is wonderful but if Egyptian art doesn't appeal, skip it. Whatever you see you will find fascinating. Guaranteed!
It really depends on what you love most. There is ancient art and archaeological artifacts from nearly every place and time in history (Egypt, Ancient Near East, Greece, Rome, Asia, etc.), enormous collections of Degas, Rodin, Rubens, and more. My wife had never been, so on our most recent trip to NYC we spent three hours going through as much of the museum as possible to give her a taste of what's there. You really need multiple visits to appreciate the collections.
I loved the ancient Egyptian period rooms and exihibit. The Armenian exihibit was very good too.
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