"Echar un trago" sounds a bit old fashioned. Not something a person under 50 would say, normally. But everybody would understand it, at least in Spain.
The alternative Mercedes gave you is correct but it's applied to any kind of beverage. However, when we talk about "echar un trago" it's normally related to an alcoholic beverage. The image I get in my mind when I hear that expression is a cowboy having a shot of whiskey in the saloon in an old western movie.
Meanwhile, "tomar algo" can be a fizzy drink, a coffee, a beer or anything liquid, in fact.