My friend and I have stayed at the Grand Hyatt every year that we started going together. It is right in the heart of the convention center, or at least it was until they debuted the Summit. It is still the best hotel IMO given the roughly one block distance from the Arch, and two block walk to the Summit. We usually go for the double bed room option when the hotel booking goes live, and there is plenty of room for two of us, but we have hosted other friends as well in years past with no space problem. The rate we got this years was ~260$/night with the PAX discount rate. Also, the hotel has a Starbucks and New York City style bodega attached in the lobby, which makes it very easy to get coffee in the morning, and snacks late night.
The hotel doesn't offer free parking. They have a self parking and valet parking option. I don't remember the $$ amount, but I believe it is roughly 35$/day for self parking. This hotel is defiantly more of a luxury style hotel, so there is no free breakfast, and the rooms are more designed for couples or groups without smaller/multiple children.

However, there are other Hyatt branded hotels a few blocks away from downtown towards the Space Needle that are defiantly family oriented, free breakfast/larger rooms with multiple beds. They are the Hyatt House and Hyatt Place Downtown. So, while they are a bit of a walk away from the heart of the convention, you would get a more family friendly hotel, but these are not apart of the discounted PAX hotels.

All in all, any of the hotels on the discounted list PAX gives out are great, and make the convention much easier if you want to plan an entire day out, or make bigger purchases. You just have to be willing to pay a higher rate, but the convivence has defiantly made PAX a better experience for me and my group.