My advice is to bring a car if there's any way for you to do so! If you don't own one or just can't, sure, you can make it work as a pedestrian in Dallas. But it ain't easy. The Highland Park/University Park area near SMU is quite walkable (though brutally expensive as far as I know), but you'd really be hemming yourself in by counting on that area to meet all your needs. Plus there are downright sketchy neighborhoods bordering the nice areas near SMU.
As for transit, the DART rail is a pretty nifty option, but its service area is extremely limited. And the bus system is lousy. It's actually very extensive, but the routes are a mess. In my experience you can't get anywhere on DART buses without tranferring two or three times.
Also keep in mind that it gets very, very hot in Dallas as early as May and can stay that way into October. Walking around in 103 degree heat can be not only exhausting but also downright dangerous. Plus the DFW metroplex is the definition of urban sprawl. If you really want to experience the city, you'll need a vehicle to get out and about to visit the places worth visiting. There are *lots* of fun things to do in DFW, but none of them are remotely close to one another. So to reiterate, bring a car if you can. You'll be glad you did. And congrats on SMU! Great school with a nice campus in a beautiful neighborhood.