Your not going to find a Sony E-Mount lens for any where near that price. Your best bet would be to get an adapter that allows you to use Sony/Minolta AF lens on the NEX body. Though that alone would cost you $50 plus another $30 or so for a cheap Minolta AF lens. The cheapest E-Mount lens you will find is probably about $100 used.
Okay. It costs $50 for a adapter? Cheese. What is the best cheap E Mount zoom lens used? It HAS to be pretty small, thats why I am buying a NEX. 3 inches, maybe 4 is my max.
Then the 16mm is probably what you need but it has no zoom but is very small. You can get the 18-55mm for the same price but it may be bigger then what you are looking for.
edit: just did some looking and the 18-55mm is under 3" tall so it should work perfect for you. You might be able to look around and find a used one cheaper.