I eventually got the chance to do that last January 31, this was during the long weekend care of our rich and vibrant Chinese culture. We started of the day at the first (yes there are actually two) museum, this is the one closest to Luneta Park or is in Luneta Park (geographic technicalities elude me). The entrance fee for the two national museums is at Php. 150, Php 50 if you're a student (public, private, undergrad, graduate whichever works your way. Just present an ID) and this fee allows you access to the two museums (yes no need to double pay but we will get to that later).
As you make your way around the museum, it's not only the material and natural culture that you should take note off. The American-era architecture also takes a hold of you and in some ways makes you forget that you're actually in Manila.
They're even open during holidays and Sunday admissions are usually free!