Koi Ponds in Sun and Shade
While there are benefits to full sun versus shade for koi ponds, don't think you can't have a pond if the only suitable site is in full baking sun, or even if you're at the other extreme and your koi pond will get no direct sunlight. You can have a koi pond in both situations, though you will want to adjust a few things for optimal success.
Because you can have a pond anywhere, let's first talk in terms of benefits - the benefits of shade versus the benefits of sun for koi ponds, then we'll go over the drawbacks and what you can do to get around them.
The primary benefit to having a koi pond in full sun is that you'll be able to have beautiful water lilies, which need at least six hours of full sun. Water lilies and other aquatic plants provide a bunch of benefits unto themselves - they clean the water, provide shelter for fish, add oxygen, are beautiful, and make a pond look completely blended into your landscape. But you will need to protect the plants from your koi - or your expensive water lily will end up as koi salad.
A secondary benefit to having a pond in full sun is that it will get warmer faster. If you live in a really hot climate, this is a drawback, but for most of us in the United States and Canada, having the koi pond thaw out a week or two early is a nice benefit.
Now on to koi ponds in shade. Shade can help reduce evaporation (so you'll have to "top-off" your pond less often). It also gives you a little more coolness. The coolness can be important, because the warmer water is, the less oxygen it can hold. If you're going to have a heavily or even moderately stocked koi pond with limited filtration and oxygenation, siting the pond in a bit of shade might be wise. However, you can get around this "overheating" from full sun by dropping an air stone into the pond on hot days. Many koi pond stores now have solar powered air pumps, so you can add some oxygen for your koiwith very little hassle.
We're moving over to drawbacks now, so its time to mention the primary drawback everyone talks about with a full-sun pond: Algae. Don't buy it. You can absolutely have a pond in full sun, with lots of fish and plants and barely see any algae. The first line of defense against algae is to not feed it - algae needs phosphates to become a problem, and ironically most of us pond keepers feed it abundant amounts of phosphates in the water conditioners we use. You'll have to be a bit pickier, and you may even have to mail order your pH adjuster, but find one without phosphates and you'll be able to put your pond anywhere you like without any ugly algae.
Another fantastically effective algae preventer is a UV or Ultra Violet clarifier. Some filter come with them, or you can buy one separately for $100 or so. A UV clarifier will kill the floating algae in the koi pond water, thus clearing the green water some ponders struggle with, and it can also be an effective secondary treatment for bacterial infections in fish. But a UV clarifier will also kill all the beneficial bacteria in the water, so you may want to hold off from buying a UV clarifier unless you've got algae or disease problems in your koi pond.
With all that in mind, frequently the best situation is to have the pond get a bit of sun and a bit of shade throughout the day. Giving the pond a bit of shade in the afternoon, when the sun is at its most intense, is ideal. This way your waterlilies will have already had six hours of sun, but your fish can relax a bit in some late afternoon shade.