Pros: Museums are (usually) really interesting and kick ass.  They can be cheap in most cases, and provide for LOTS of opinionated conversation.

Cons: Lots of walking, lots of talking.  If the date turns sour, your pretty much fucked

Notes:  Go to a GOOD museum!   If you can, look up reviews and ask people who've been before.  Don't go to a dull museum without much color, go to one that has a lot of color variations, interesting things (like fossils), art, etc.