It depends on how much you want to spend. The Sony ICF-CD73 received a maximum 5 star award when reviewed by the Radio Listener's Guide and either 4 or 5 stars from the people who've reviewed it on the Amazon website:
http://www.amazon.co....UTF8&showViewpoints=1
It's got AM and FM bands, with a CD player (which recognises CD-R & CD-RW disks, so that you can burn your own favourite tracks to CD on your computer), with 15 presets and a clock. The only problem is that, at about 70 quid, it's far from cheap!
Basically the same radio without the CD player is branded as the Sony ICF-S79W, costing £57.74 and well-reviewed on Amazon:
http://www.amazon.co....UTF8&showViewpoints=1
For good reviews at a lower price (£13.09), check out the silly penguin here!
http://www.amazon.co....UTF8&showViewpoints=1
Chris