Free things to do
Hong Kong has a genuinely long list of things worth doing that cost little or nothing beyond a transport fare.
Views
The Tsim Sha Tsui promenade gives one of the best skyline views anywhere for free, and many of the city's hiking trails — including sections of Dragon's Back — offer harbour and coastline views without an entry fee.
Museums with free or near-free entry
Several government-run museums charge only a nominal fee or waive it entirely on certain days — worth checking current entry terms before visiting, since these do change.
Temples
Most working temples, including Man Mo Temple and Wong Tai Sin, are free to enter and walk through respectfully, though a small donation is customary if you're lighting incense.
Markets, for browsing
Temple Street, the Ladies' Market and the Flower Market cost nothing to wander even if you don't buy anything — genuinely enjoyable simply as street life.