You can have a look at Wikipedia (US passport/Brazilian passport). The color codes are a bit different depending on the map but everything in dark green is definitely OK to just drop by and by combining both passports, that includes the Schengen area and most of Europe, most of South-East Asia, Japan, Korea…
Yellow (“visa on arrival”) means you will have to pay some money but can still drop by without advance notice. India or Australia require some form of prior authorization but it can be done online in a matter of hours so you can still more-or-less decide to go there on the spur of the moment. Obviously, some countries like China still require a proper visa so you cannot go there without some preparation.
The Brazilian passport is actually not bad and nicely complements the US passport. It affords you even broader access to South America and a few things people from the US and most of Europe do not have: visa-free access to Russia and visa-on-arrival in Iran. Also visa-free access to Turkey (even if the Turkish e-visa really isn't much of a hassle, that's even better).
One thing to note is that when using visa-free or visa-on-arrival facilities, it's often required to be able to present a ticket out of the country on entry (and even when that's not strictly speaking required, it might come in handy). So you do need to either purchase some cheap/refundable ticket you feel comfortable dropping if needed or to plan one move ahead (look up “onward travel” in the archive for more details and country-by-country advice).