As I write this I am working and residing in Kaohsiung, the 2nd largest city in Taiwan and 3rd largest shipping port in the world. The city has a nice layout with broad palm tree-lined boulevards, great outdoor cafes, street markets, decent clubs. I recommend spring or fall as the best times to visit, as in the summer the heat & humidity can become unbearable, and in winter months the air pollution skyrockets.
Favourite spots:
Monkey Mountain to see the 1000+ wild macaques and get a great view of the city, sunsets at the Sun Yat-Sen University breakwater, the Cultural Centre for free outdoor events, Chichin Island for the black sand beaches and fresh seafood.
What's really great:
My favourite thing about this place is how helpful the locals are. Also, there's just the sheer convenience. If you need to eat, shop, go to the internet cafe, hop on a bus to anywhere on the island etc. etc. it's all available at any hour.
Nightlife:
Voodoo lounge, nice atmospere, spacious, good seating.
Hangouts:
Bar 65 for the fabulously hospitable owner John and the laid back friendly vibe.
Restaurants:
Hotpot restaurants all over, Thai restaurant in Fuhong Alley, seafood restaurant just before Sun Yat-Sen University, Smokey Joe's for American grub.
Other recommendations:
Maolin up north in the mountains for hot springs and waterfalls, Kenting in the south for sun, sand and surf.