I don't think there are any bad parts of town in Grapevine. You can find apartments all over the place near the Grapevine Mills Mall. My stepmom and brother used to live in a two bedroom for about $1,000 a month on Grapevine Mills Blvd. right across from the mall. A little older, 80s maybe, but nice with a gated entry pool and grills.
They also lived in a place up the road, Grapevine Mills Parkway, Camden River Walk apartments. NICE places. They had a two bedroom with a garage for $1,250 or so. That place was REALLY nice.
If you can get out here for a weekend to look around then you'll find places easily. It's by no means ghetto.
Where in Grapevine are you going to be working? You might want to look at Euless if you want cheaper. Grapevine is just north west of DFW airport, and traffic on 635 is slow in rush hour. I would not go east of Belt Line in Irving, or much South of 114. But, prices may force you towards Euless/Irving. They're not bad areas either. Don't listen to the people who tell you Irving is a ghetto or Euless is a ghetto. Personally I would stay towards Grapevine or Euless. Depends on how much room you need and how far you're willing to drive.