Re-Hai rock climbing site is just in Taipei city, the view up there is so great, you can see whole Xinbeitou area.
Hop on an MRT(Taipei metro), go to Xinbeitou station, enjoy this half day outing.
You will do, a short hiking / experience two rock climbing routes / one 20 meters high rappelling route, enjoy the view and a good day.
You can choose this tour to be in the morning or in the afternoon.
For the other half day, you can visit Xinbeitou Area (not included in this product), It's famous for hot spring resorts / the thermal valley (a pool of hot spring source) / A nice park with hot spring stream in it / Public hot spring pool / the hot spring museum / Beitou library. Worth to spend a half day.