I did a lot of research when buying mine (a year or two ago). I ended up with a Canon PowerShot SX110 IS, which is pretty much perfect for me. Point-and-shoot enough that I don't need to know much, enough zoom, megapixels, and speed for what I want to do with it.
It takes really fantastic pictures, and was in my price range (somewhere between $200-$250, I'm sure they'r a bit cheaper now).
Here's a shot of an owl my son spotted, taken from very far away. The camera has 10x optical zoom, 3x digital zoom, bt the optical stabilization is good enough that even when you zoom all the way in the pictures are fantastic!
It does nice close-ups, too.
I really recommend Canons, and for this price range this is an awesome camera!