Prices for traveling from the US

I am wondering what are good prices to pay for traveling from the US (probably Chicago) to Taipei at the end of June? I looked on this forum, and I saw that last summer, they were quoting prices near $600(USD), but when I am looking (online), I can’t find one way tickets that are less than $600, and round-trip tickets are all over $1000.

So I guess I have the following questions:

Would you recommend buying a one way ticket to TPE (with an open ticket to Hong Kong to get past the authorities)? Or buy an open ended two-way ticket (which I think would be closer to $1300, unless you guys have any good tips)?

What is a good (or at least a decent) price to pay? Would you recommend any web sites or travel agents?

If I opt for the one-way to TPE, and the open ticket to Hong Kong, would I need to have a date on the Hong Kong ticket that is within 60 days of my departure, or could it simply be “open”?

Thanks for any help, as you can see, I am clueless!

I think that’s just what the going rate is. I paid about 1,000 for a round trip ticket that will be departing D.C. this coming weekend, but I had to pay for it three months in advance. Otherwise, the prices were about $1,200 to $1,300 U.S. I was quoted the same rate for various dates throughout the sammer (round trip).