A lady's journey to Taiwan, spanning across North to South of Taiwan, best done in the Summer (June to September) because it includes the lovely beaches of Kenting. I like this for the visits to the farms and countryside and the beach, brilliant! This is perhaps the most unique Taichung travel plan I've seen, but the farm visit requires a guide or taxi driver for English speaking tourists. Itinerary covers:

Day 1: drive to Taichung (Ladybug Organic Farm, Dongshi Taichung) + Sweet Charm Winery

Day 2 & 3: Taichung to Tainan (Sicao Green Tunnel Cruise)

Day 4: Tainan to Kenting 

Day 5 & 6: Kenting to Changhua (back to Taipei) (Fairy Lake Leisure Farm)

Day 7: Taipei

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For those interested in exploring organic farms in Taiwan visit WWOOF.

Please know that this itinerary requires booking a taxi driver guide, at least from Taichung onwards.