Hi!

if you want to see something more than the usual American downtown - which is kinda neat in Dallas anyway, I'd suggest to head outside. Otherwise, both the aquarium and the Art Museum (above all this last one) are worth a visit. White Rock Lake is a cool area with a dam and all the green around also interesting for a good walk. It's full of animals (I even saw pelicans over there last year).

As far as other places around Dallas, Fort Worth has got a nice zoo, while Arlington has a Six Flags, which I guess you know it's an amusement park where you can find all those weird fried thingies Texans do love so much...

Hope that helps as a start