Cheryl,
I've recently upgraded from a Kodak DX6490, a 4 MP, 10X Optical zoom camera to a Nikon D50 DSLR. My daughter and I went together on the Kodak a couple of years ago and overall was quite satisfied with it. I was looking for something with higher resolution, considering Kodak P850 or the DMC-FZ30 that Ron mentioned.
I wanted/needed the long lens capability (lots of Oshkosh aircraft shots) and with the DX6490 did not always have the resolution I needed with the long shots there. The P850, FZ30 both give you 12X optical zoom, optical being the only one that counts ... with the image stabilization a big plus. Also the video capability was nice, something I originally didn't think I would use, but found it quite useful. Not near the quality of a regular video camera, but handy non the less.
The downside of the DX6490 was shutter lag, and relatively slow focusing and only 4 mp compared to 6 or 8 mp available now for about the same price as the 6490 originally.
While I was originally looking for a similar replacement it was suggested I look at a DSLR.
Advantages of the D50 is almost instant on, much faster auto focus, manual zoom, manual focus available, 6.1 mp, and much less shutter lag, 2.5 frames per second (try to time those ribbon cutting shots at Oshkosh with the built in shutter lag

) . Has basically the same mode options as the Kodak, etc ... from point and shoot to full manual ... but lose the video option.
Anyhow, Ritz camera had a sale going mid December and I ended up with the D50 body with the 28-80mm kit lens for $649 after rebates. Added the 70-300mm Nikor lens to that, another $175 or so.
I'm still learning to use all the modes, many years since I was into this seriously (old Mamiyaflex 2 1/4 square from the 60's) but am happy so far. As always faster lens would be better, that hasn't changed since the 60's
Here is a D50 review site
<http://www.dcresource.com/reviews/nikon/d50-review/index.shtml>
The D50 is considered an entry level DSLR, either way D50 or P850 etc I think you would be quite happy.
FWIW ....
Howard