Choosing miles means you are not eligible for G offer bonus points.

You can not earn both miles and G bonus Gold Passport points.

Here is the link to Hyatt Gold Passport current G bonuses for people who don't know where to find the G bonus offers.

Use the G bonus links to make your reservation in order to earn additional bonus points at a participating Hyatt property.

While we generically use the term "Gx bonus" referring to Gold Passport hotel points, some bonuses are "A" miles bonuses. You can also earn bonus miles at participating properties offering "A" bonuses.

Great tutorial SanDiego1K. I will link to it on my blog.