Highly recommend it. I mainly lived on the northwest coast—it's a great place to be. That insanely high mountain that runs down the middle of the island generally takes the brunt of the typhoons coming from the east, and they spin off to the south.

That said, I'm not a fan of maintenance roads without guardrails where big trucks (who are not supposed to take them) will have no problem putting their wheel up on the mountain—with your car on the cliffside of barely a one-lane road—to pass. I will never take that northwest to northeast trip over that mountain again, but it was beautiful, so far above the cloudline. There's a massive ancient tree all the way at the top, just next to a hot springs place. It's pretty majestic.

My brakes burned out corkscrewing up the mountain at night, and we met a very nice guy who owns a produce store up there and does rescue for people who get stuck. He let us come in at 11 PM, made us some tea, and we talked while waiting for my brakes to cool down. Overall, Taiwanese people are some of the friendliest I have ever met.

And most definitely, one month will give you plenty of time to see the sights and meet the locals. It was not uncommon to see people circumnavigate the island on their bicycles—I even once met some teenagers who were guerilla camping and doing it by skateboard for their blog.