I can absolutely recommend FujiFilm cameras - particularly the FinePix F20 model and above. I'm not sure what the latest incarnation is called, but they have progressively become F30, F31, F40 and so on. My F30 cost me about £90 from Amazon.com last year and people are always amazed by how good the photo quality is. Video quality is also superior. Indeed, my father bought the F20 model as a result (the only difference being a minimal reduction in ISO rating and a slider button instead of a knob selector).
They are renowned for a high ISO rating which means great shots in low light and tend to have at least 7 MP. Another bonus is an internal lithium battery, so you don't need to buy AA batteries all the time to charge it, you just plug it in and charge to get several days worth of use - I only charged it once or twice on a three week holiday sightseeing last yr.
From readings I've done, the general concensus is that you don't need any more than 6-7 megapixels if the camera has an optical zoom lens of x3 because the lens physically won't be able to accomodate any better photos with any higher megapixels... so don't be too hung up on having 10 MP or anything like that unless the lens is up to it.
This site is amazing for reviews if you have an idea of a camera you like:
http://www.trustedreviews.com/digital-cameras/