Kent sez, "Here's a travel hack that came to me all at once in a flash at SxSW this year: how to make cold-brewed coffee out of the horrible filter pack and inadequate equipment you often find in hotels in the USA."
Kent's method is clever and upside-down-y, but I still like my method, which involves using your own coffee and a disposable plastic breast-milk bag.
Carefully unwrap (don't tear!) one or two of those premeasured filter-packs that came with your coffee service and stuff it gently into the cup. Ideally you want four parts water to one part coffee, but this is tough to estimate with filter packs.
Fill the remaining space in the cup all the way up with water. Tap water works; filtered or bottled is better. Try not to leave any air bubbles.
Don't worry if it seems it will result in a tiny amount of coffee; it will be concentrated, intensely flavored, and—assuming you're not stuck with decaf—highly caffeinated.