Help with Digital Camera - Cybershot or Nikon?

I'm looking for a new digital camera. I've had a Kodak Easy Share for a few years and need an upgrade. What I like about the Kodak Easy Share is the good zoom, but it takes horrible photos if the light is good (evening, gymnasium, night) and when you zoom so far it takes blurry pictures. I'm looking for a camera with a good zoom and that takes good pictures in the day time and night time. I do like that the Easy Share has different settings (landscape, sports, night, etc.) that sometimes help the picture quality. And, I can take short videos on the Easy Share so I want that capability in my new camera.

I've heard good things about the Sony Cybershot and Nikon cameras. Can someone recommend one and why? My budget is $300 or $350 and LESS. Thanks!
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