I've done this a few times successfully. We always start with Canada for lunch on the day we're there, since the beverage selection is much better in the restaurant than outside. We also start here because the margaritas in Mexico are dismal (just tried AGAIN two weeks ago because I like to torture myself and it was just as bad as always) and it's best if you can't taste them. Same with the beer selection in Mexico.
From there, what I ususally do:
UK: Guinness
France: red wine
Morocco: Tangierine Cocktail
Japan: up to the Matsunoma Lounge for a Samurai (plum wine, vodka, lime juice). The drink selection here is fair, they have a full bar, beer, and wine.
US: usually skip and make up for it somewhere else, but if I'm going to, a Sam Adams. Drink selection is sad here. :/
Italy: red wine or limoncello
Germany: beer and shot
China: Tsingtao
Norway: Carlsberg or Viking Coffee, depending on what time of year it is
Mexico: icky margarita or weak Mexican beer, but at least I can't taste it.
I have no issue mixing beer/wine/liquor, and I'm a girl. I make sure that I go slowly, have one drink per country (except Germany, but shots there are usually fun), drink a lot of water, and eat to slow down absorption. Vitamin B pills are your friend.