GIKI and NUST are both ok. I did it from UET Taxila, and now I'm in France for a PhD on diesel engines. It really doesn't matter in Pakistan, as long as you are willing to work hard for it. Try to chose a MS course during our BSc, so you have time to prepare for GRE, TOEFL etc, on time.
Try to get a normal BSc. Mechanical Engineering degree in Pakistan. Don't go for Automotive Engineering as BSc. It's not as useful as a traditional Mechanical Engineering degree.
Hope this helps, feel free to contact me if you need any other info.
Wassalam,
Sami