The Nikon Coolpix S8100 will be $149.99 at Best Buy and it looks like a great option for you. It's compact (pocket sized), but has a 12x zoom. The quality of the camera will be very good, as well. Most pocket-sized cameras right now have a max 5x optical zoom.
I would consider a 10x to be the minimum optical zoom for a "primary" camera. It makes a huge difference for those shots where you can't get any closer to the subject (at the zoo, for instance).
12x is all the better, of course.