About 3 years ago we purchased a cool bag from La Sirena for about €5. It has gone all over the world with us, and has paid for itself a hundred times over. We can take it to the beach filled with drinks and ice, and by the end of the day the drinks are still cool. If left in a hotel room and out of the sunlight, I imagine it would work even better.
Failing that, a decent sized bucket would do the trick - and it wouldn't piss out everywhere.
In the past I have used the sink trick above too. Line the sink with foil to keep the ice cooler for longer. Does become a pain when you want to wash your hands, mind.