Flying to DFW or Love Field or driving your own car from home?
http://www.hoteladolphus.com/transportation-directions
The hotel is within walking distance of many things you might want to see downtown. Would it make sense to take a taxi from the airport?
If while you are walking around, you find a much better price move the car if you don't like the price at the Adolphus.

Here are two listings for parking lot companies. Give them a call. They each have a lot within easy walking distance to the Adolphus.

PLATINUM PARKING
(214) 749-1280
http://platinumparking.us

ALLRIGHT PARKING
(214) 744-6168

You might want to confirm whether they allow 24 hour parking.

I had an office in the Adolphus Tower until a few years ago. We never found 24 hour parking that was significantly less costly than the hotel parking for our overnight guests. (They were mostly out of town experts.)

More importantly, because the area still does not have significant foot traffic outside of business hours, our guests reported being uncomfortable walking from remote parking back to the hotel after dark.

That said, there is a lot directly across the street from the entrance to the hotel parking on S. Field street(not the hotel valet entrance on Commerce) which used to allow 24 hour parking and allowed direct entrance into the hotel.