flyertalk.com has lots of discount codes. Some you have to be a member of something, some you don't.
You also could look into a "Stay Certificate". Basically it's like prepaying for your stay based on # of nights. When you check in, just hand over the cert & it includes all taxes. Be sure to book stating you want to use a stay cert. Availability is not same as paying cash. They only allow so many rooms per nt on this rate.
You may want to read the Terms & Conditions listed under
"Certificates For Stays Of 1 To 5 Nights Or More" https://www.certificates.hyatt.com/Default.aspx
The DFW Hyatt Regencey accepts the "classic" level cert which is the least expensive. (see Participating Locations for complete list.)
It's $109/nt + shipping the certs to you. Remember this includes all taxes.
They are non-refundable so make sure they have cert stay availability for your date before buying. They used to expire but I believe now they don't.