Taj:
Based on your want to be near shopping malls and restaurants, you should look into North Raleigh neighborhoods. It is close to downtown Raleigh so you will be paying a premium to live there. I am around your age and can say that the majority of our friends (with and without kids) live in that area - specifically, Five Points and North Hills. Cary sounds like it could be a great alternative as well. If you are in Durham and traveling back and forth to Knightdale more than infrequently, you may get tired of that travel. Living in Raleigh or Cary will certainly alleviate that issue. Do you know yet where you will be working, or are you working from home?
My wife and I relocated to Raleigh about a year ago. We had similar considerations and actually ended up in Boylan Heights, which is only a 15 minute walk from DTR (downtown Raleigh). Boylan Heights is near Cameron Village, which has all of the shopping/activities you could ever need, plus access to downtown. My only word of advice on Boylan Heights is that it is adjacent to NC State, so you will regularly encounter the college crowd. I never had an issue with that, and I know some people would like to avoid that altogether. Our rent was $1,750 for a 2-bed ,1,250 square foot townhouse, so a 3-bed will be slightly above your budget in that neighborhood.
We love it here so much that we bought a place across the city in East Raleigh. We are city people so being close to downtown pushed us towards those two neighborhoods.
I hope this helps. Feel free to reach out if you have any other questions or need help in the relo!
Will