I bought my wife one of these for her birthday
http://www.pixmania.co.uk/uk/uk/29876/art/nikon/coolpix-3100-including-re.html
And I have to say I am really impressed with it. Its really small, easily pocket sized, and takes nice pictures, and has a credible 3x optical zoom.
I myself have a Fuji with a nice 6x optical zoom, but its big and bulky, and I didnt take it to Florida with me as I couldnt be bothered with carrying another bag with me.
The main thing with digital cameras is to ignore the "digital zoom" features and look only at what "Optical zoom" it has.
Whatever you do, never buy one that doesnt have an optical zoom.
I would also say make sure you buy one from a recognised camera manufacturer, who know what they are doing regarding optics.....similarly, avoid misleading mega-pixel statistics such as "effective pixels" or "interoplated pixels"...you might see "6 megapixels effective, actual 3 megapixels", so ignore the 6 bit and treat it as a 3......this method of advertising is reminiscent of the 80's ghettoblaster phenomenom where the manufacturers found new ways of expressing the Watts power output of their systems, in order to look better than their competitors.
And when it comes to megapixels, 2 is fine for normal sized snaps, 3 is a good number to look for though for a non slr camera.