Just to chip in my twopence on the Zhongli front specifically:
River is pretty much the only place you’re gonna find in town, but landlady Kim is a good egg. Don’t be a dick and she’ll look after you and make sure you have a good time there. She also runs Ocean Cafe which is an alright hangout during the day. 2 or 3 other bars have also opened up on Datong Road, but I’m yet to go in or see anyone in them.
Hideout just over the road in the centre of Zhongli Park (next to the basketball courts) has an ok vibe, they try to pitch themselves as an upmarket cocktail bar (with prices to match). A few expats hang out there, but its basically more a stop gap if you want somewhere to hang out before everywhere else opens.
The Jalapeno run by Jack over by the Kuva Chateau hotel attracts a lot of westerners who are here on business, but not many expats. He spent a long time in LA, good English and his Mexican bar snacks aren’t so bad. For the same western crowd you can also hit the bar in Kuva Chateau itself.
After that you’re really scraping the barrel.
If you wanna get smashed off your face, dance and/or hookup go to the Search nightclub, normally a few expats in there looking to do just that.
I learnt the other night there’s a weekly bowling league with a few expats going on at Bowling Alley - you can rock up and play a friendly with some of the other guys there who wanna play occasionally but aren’t in a league team - I’ll edit the details in here when I can find them.
After that head to the neighbourhood around CYCU. Massive night market and a few student bars operating around there, you might find a western student or two, or at the very least some Taiwanese who speak ok English. Idea, The Voice and a bar that constantly changes names (roughly here on the map, currently known as Bar Hao) are your best places to try.