In general, I'd say the travel zoom type cameras mentioned above might be a good category to look at - smallish and portable, but with big zoom ranges for flexibility, and most would have decent image quality for nice prints or slideshows.
If you want something with a bit more of a grip and chunky design, look at the superzoom cameras like the Canon SX20, Nikon P100, Sony HX1, Panasonic FZ35, Fuji HS10, etc. Those have even bigger lens ranges, and are fatter and chunkier to hold onto.
I'm afraid the other piece of advice is to learn more about photography in general, which will greatly improve your photos. Whether you are looking at photos online from a DSLR or from a P&S, when you see a really great photo that makes you say 'WOW!', it isn't the camera that did it...it was the photographer. A great photographer could take your Kodak and probably churn out a very nice photo, and a terrible photographer could grab a professional DSLR with a $20,000 lens out of the hands of a
National Geographic photographer, and take a horrible photo. Trust me, the brand name and model number of the camera are not the thing to judge when looking at photos. Not all cameras are alike and some are better than others - but it comes down to getting the features you want, the lens range you want, the body size and design you want, and fitting into the budget you want. Brand name means nothing towards getting a good photo, and doesn't guarantee a good camera - all the major brands make cheapo cameras and really good ones, and everything in between!