Arlington to Mesquite is a 30 mile straight shot down I-30. The real issue is how long it will take you to get out of the parking lot, but you'll have that delay no matter where you stay. Once out of the lot and onto I-30, it should be highway speeds (60-70 mph) the whole way.

If you're looking for casinos, you'll also find some in Louisiana, both in the Shreveport/Bossier area that you'll likely be passing thru, as well as in New Orleans (there's a Harrah's right downtown at the foot of Canal St).