I'm only allowed to visit Guernsey if I promise to bring back some perfume for my wife! There are several shops to chose from, but I always visit Au Caprice Perfumerie as they always have such a good selection.
What to buy: Until the change in 'Duty Paid' rules some years ago, Guernsey was the ideal place to purchase wines and (dare I say) tobacco products. However, these are just as costly as in UK now, plus you have to cart them home.
Perfume appears to be a good buy, as it is VAT free, and usually there are some special offers to be had.
Update May 2014: Don't be conned if you come over on the Condor Ferry. Their Duty Free shop lists a particular perfume that my wife likes at £39 for 100ml. The lady said 'much cheaper than elsewhere'. However, for exactly the same brand and quantity in St Peter Port you will pay only £24 or so.
What to pay: Cheaper than in UK
Address: In the Main Street
Boatworks is the main Ship's Chandler's in St Peter Port. They have a large shop with almost everything you will need for your boat, but, again, the prices will be higher as the items have to be imported.
This is the only place that you can refill your boat's fuel tanks, and here you will get a saving on the fuel prices, as there is not the same amount of tax to pay as in the UK. Cans can not be filled here, except on board your boat, so don't walk around with a 5 litre can and expect to get it filled.
What to buy: They have everything nautical, and are always very helpful.
What to pay: About the same as in UK
Address: Castle Emplacement, St Peter Port
Directions: South side of the marina, walking towards Castle Cornet.
Shopping in St Perter Port is almost like being in a large town in the UK. Most well-known 'brand' shops are here, including Boots, all the main banks and so on. Some shops are aimed at the casual tourist, with 'kiss-me-quick' type wares, buckets and spades and so on. Others are more high-class including the various perfumeries. There is a co-op food store further up into the town, above the church, just past the HMV shop (which may well now be closed).
What to pay: Because the Channel Islands are not part of the United Kingdom, nor part of the European Union, there is no value added tax (VAT) to pay. However, as almost everything has to be shipped in the prices in the shops can be as high as in the UK. For instance, a Cornish Pasty will cost you about £1 more!