Well, I’d suggest some decent waterproof gear, as it rains a fair bit here. Umbrella’s aren’t always enough. Get a pair of Gore-tex shoes, you’ll be happy you did. Not the heavy stuff, the thin ones, I think they call the Gore-tex in them XCR or something like that. I had a pair when I moved here and used them almost every day so they got worn out, but I’m going to get a new pair once it starts raining again, as I hate having wet feet.
I’ve only ever been to Yilan once, but it looks like a nice little coastal town. They seem to have most things there, but it’s not a huge place. Luckily it’s not too far from Taipei and there are buses that goes in-between. I hope you won’t mind the 12km long tunnel though…
Have a look at my blog (link below) for links to the major grocery stores in Taiwan. It’s all in Chinese once you find the sites though, but at least it’ll give you an idea of what’s available. There should at least be a Carrefour and maybe some other of the larger supermarkets there and they all have a small selection of imported food. For other stuff you’ll have to go to Taipei, or even abroad. At least HK isn’t far and you can get most things there.
You might also want to be aware of the fact that most food here contains pork fat, as even the local bakeries use it in their bread and vegetables if quite often fried in it. The locals rather not eat beef over pork, something to do with the oxen being a farm animal that helps the farmer on the field or something and you can’t eat that…
Just a heads up, that’s all.