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Per the Taiwan CDC:
arriving travelers shall also provide proof of the place of quarantine where travelers stay to undergo quarantine (in principle, the place of quarantine shall be a quarantine hotel or a group quarantine facility where they plan to stay at their own expense); they should take quarantine taxis at their own expense or get a ride from their friends, relatives, companies, or organizations to go to quarantine hotels or group quarantine facilities after arrival.
So you can quarantine anywhere, but you need to use a dedicated transport to get there, you can't use public transport. This either means arranging some sort of charter ride to Tainan, which will obviously be expensive since it's literally at the other end of the island, or quarantining in/near Taipei.
Have you considered flying into Kaohsiung? It would be much closer to Tainan.