Ken Rockwell has some good recommendations in your range: http://www.kenrockwell.com/tech/recommended-cameras.htm.
The Nikon D3100 with 18-55mm zoom might fit your needs and budget.
Hey!
Oh no! Not Ken Rockwell

When choosing a camera, there are many considerations beyond the size and performance of the sensor. As former owner of a few NEX cameras, I would not be so quick to recommend them. The user interface is very awkward. If you can wrap your head around it, that is one thing. Getting use to it is quite another thing. NEX wrote the book on menu diving.
OTOH, they can produce exceptional high quality images (with the right lenses) and they are much smaller and lighter than DSLR. This is why people are drawn to them in the first place. But the convoluted labyrinth menu system makes day to day operation and handling a serious PITA, and that is what drives many people away from them.
I don't own any Sony NEX but I did play with them a few times at B&H. Yes, they are lots of things on menu. But I didn't find it too hard to get around it. Well, maybe because usually I've never use most of the features on the camera, usually you'll see my cameras set at either Manual or Aperture priority.
But I can see some people who like to use special features on the camera spend time getting to it. Not sure how the new one will be.
Crazy - in three days this camera has jumped up $40 in price. I am trying to make a case for my brother, who has a budget of around $100 for a camera, to get this and the $40 price jump did not help...
Yes, that's crazy. Believe or not I have seen this one listed as high as $499 on B&H for a while. Don't know why this model's price fluctuate often.
Too bad it was a great deal at $298... funny that Sony sell that kit zoom by itself more than that.
Take care,
Buddy