Amsterdam for 4 days and (Fill in the blank) for 2 days?

I actually think that 4 days in Amsterdam is too much! I first visited Amsterdam many, many years ago and then recently for a day. Walked across city from the Van Gogh Museum to the Central Station . Boy has this city gone to pot (literally and figuratively!!)
It was charming on first visit but not anymore. The 2 museums are very worthwhile but really only need a day. I agree with Kent that Bruges is fantastic. Would go back in a minute. Check on train service there from Amsterdam. (we drove from Brussels)

I would also vote for Bruges. It is lovely and doable in 2 days.

I'd opt for a visit to the open air musuem in Enkhuizen (see rick's recommendation). I live fairly close to A'dam and the trip to Enkhuizen itself is worthwhile as it leads through the dutch countryside.
Also, just north of Amsterdam, the "zaanse schans" is worthwhile. Brugge is also very nice, but is a 3 to 4 hour drive from A'dam.

Excellent advice from the gals and guys. My two cents, use Haarlem for the home base and do all your NL stuff from there. Bruges certainly worth the trip but two full days in town, for me, would be enough; 4 in Amsdm, too many IMO. To give you an idea of time, we're into Holland for 4 nites in the spring, using Den Haag as home base and will see Amsdm, Keukenhof, Haarlem, Leiden, Delft, and Den Haag (including Scheveningen) in that time. With another day/nite, could have done Bruges as well. Although I lived in NL for a few years, and know the terrain, my wife hasn't, but I still feel she'll see plenty without feeling rushed. What's left we'll save for the next time. Have fun!