In laws are from Fort Worth. It is a great town. I'd recommend Rodeo Goat for craft beers and burgers. Railhead, Hein's and Angelo's for BBQ. I'm also partial to Martin House' Daybreak (beer modeled after a bowl of cereal) and the Imperial Texan beers.
I live in the area and play at ATC occasionally. Like many of the older courts in North Texas, they are slightly on the fast side with medium bounce (I haven't played there in the last year so this could have changed if they were resurfaced). As mentioned, the courts are in a pretty open area and so it can get very windy. Even though it's not a high elevation or dry climate, balls do tend to fly more than you would think. My kids always loved to play in other places because it was much easier to keep the ball inside the lines.
There are several public parks in Arlington that have courts you can use for a pre-match warm-up. There are also some schools nearby that may have open courts.
There are a lot of fast food and higher-end chain restaurants within 5 minutes south and southwest of the center (as mentioned, the Highlands and Parks Mall).
If you have never been to DFW, there are many Texas-ey things to see and do. Close by there are lots of bar-b-que (Babes, etc....) and Tex-Mex (we like Abuelo's) eateries in addition to some great steak houses (Chamas do Brazil). Joe T. Garcia's, just north of the Stockyards in Fort Worth, is the most famous Mexican place in the area but definitely on the milder and less adventurous side. The ambiance is nice but the crowds aren't.
In Fort Worth there is, of course, the Stockyards for a taste of the Old West. Sundance Square downtown is a very mellow place to hang out and chill in the evenings. The Botanic Gardens are beautiful and worth a visit and, very close by, the Fort Worth Zoo is one of the nicest in the country.
In Arlington, the Death Star, also known as AT&T Cowboy Stadium, is really worth taking the tour. Six Flags over Texas is 10 minutes north of ATC and close to the stadium. They are open Friday nights through Sundays in October for Fright Fest (and even some Thursday nights).
As far as Dallas itself, most every visitor still goes to the JFK assassination sight and tours the book depository by downtown at least once in their life. The tournament dates coincide with the State Fair of Texas, which is the biggest state fair by far and certainly worth seeing (be prepared to take a whole day and deal with big crowds and long lines, especially on weekends). In addition to the standard fair fare (sorry), there are lots of exhibits, live music, and a huge auto expo. Deep Ellum has a pretty wild late night scene if that's your thing, lots of bars and live bands, mostly alternative rock. Lower Greenville Avenue has some nice quaint restaurants and bars while upper Greenville has lots of dance clubs for the younger set. There are, of course, plenty of country bars in the metroplex and even some good jazz clubs. The Dallas and Fort Worth Symphonies and even Dallas Opera are in season in October.
Traffic is bad so check apps and allow extra time to get places, especially during rush hour. There is a connected rail system for DFW but it doesn't really help that much for the tournament since it doesn't go into Arlington. It works well for going to downtown Dallas or the state fair, though.
With Arlington being such a tourist place, there are a plethora of lodging choices within a reasonable driving distance. If coming during the Texas-OU weekend, though (10/5-7), you will want to book well in advance as hotels get harder to come by. 10/6 would not be the day to go to the fair as the Cotton Bowl is in the middle of the Fair Grounds. In fact, Dallas gets really crazy that whole weekend so it is not a good time to visit there unless you just love massive, rowdy crowds of drunken college students (Arlington and Fort Worth are still fine, though).
DFW is a huge metropolitan area with close to 8 million people so there are lots of other things to do. It's so spread out, though, that it's easy to miss things unless you know what you're looking for (if flying in, you will definitely want to rent a car). There are many museums, art galleries, and cool things to see (Fort Worth Water Gardens, cattle sculptures in Pioneer Park in Dallas, Dallas Heritage Village, Las Colinas Canal Walk, Mavericks and Stars games, the new Cowboys Training Center in Frisco, etc....). There are also many ultra-nice high end places to shop in Dallas.
Feel free to ask any questions (and, no, I don't work for the tourist board).