The Fountain of Happiness Square was an area of Paradise Towers.
The Seventh Doctor and Melanie Bush encountered the Red Kangs for the first time there. They were taken prisoner, but before they could be led away to the Red Kang brainquarters, the Caretakers launched a raid on the square to cleanse it of kangs and wallscrawl. This forced the Kangs to flee and in the panic, the Doctor was taken prisoner by the Caretakers.
Sometime later, Mel and Pex arrived in the square while heading for Floor 304. It was at this point that Mel questioned how well he knew the directions and also inquired as to why he was the only inbetween in the area.
Pex lied in telling her he had the power to protect invested in him by powers he was not allowed to name. He offered to demonstrate his prowess by breaking the titular fountain, but Mel asked him not to. They then continued on their journey. (TV: Paradise Towers)