Just research the metro line connections over the internet

I went on Monday. Baths are open but they have a break time for 30 min every 2 hrs,it's says that on Google as well. Thermal Valley is closed on Mondays

Yes kids can go in the designated area for hopping in the hot springs pools! I think there is no cost! I hope this helps, enjoy.

"Takinoyu" is open to the public, but no room for staying, not a hotel. The admission fee is less than US$10/person. It's nice to enjoy the hot spring!

Beitou hot spring

Nope no entrance fee, thank of the location like an neighbourhood but with hot springs around instead. No issue for animals, just got to leach them.

Beitou Outdoor Public Hot Springs 露天公共温泉 No. 6, Zhongshan Road, Beitou District, Taipei City, 112 02 2896 6939 The public out door hot springs are at the far end of the park away from Xinbeitou station. Also labeled Millennium Hotsprings. Visits are done in 2 hour sessions and the line grows until the previous groups’ time is up. Then everybody leaves en masses and it’s the next groups’ turn. These are outdoor & public so bathing suits are required, along with 40ntd.