Finding the right place for a concrete fixture like a bench or birdbath involves more than just finding an open spot in your yard. The type of fixture affects the location somewhat, and the area surrounding the fixture harbors a few major considerations. What you need to find is a spot that will help the fixture stay in good shape while not creating additional problems for you to solve.
No matter how flat your yard looks, each part of it has a slight slope. This is to facilitate draining. You need to be on the lookout for two conditions. One is that the fixture is placed in an area where water will drain away from the fixture and not toward it or your house—though you may see water drain away from the house and past the fixture.
The point is that any water on the ground headed toward the fixture should move past it and away from the rest of your property. The other is to ensure the ground immediately around the fixture is stable and will not settle, creating a depression that would allow water to pool. Not only would that water be damaging to the fixture, but it could become stagnant and harbor mosquito larvae.
How close are the sprinklers in your yard, if you have them? Concrete can develop mold, so the fixture needs to be away from sprinkler spray if at all possible. For birdbaths, which are supposed to hold water, you want to move the fixture away from sprinklers so that the water spray doesn't scare off birds.
Whether or not you place the fixture in the shade depends on the type of fixture. Benches do well in full and partial shade because the shade provides cover from the sun. Birdbaths should be in a more open area, sunny or partially sunny—meaning that while there might be some shade, there is mostly sun—so that birds see it and so that the water doesn't become stagnant as quickly.
Shade reduces evaporation, but that also means the water will sit in the bath longer. Statues can go either way; just ensure there's good airflow around them to prevent mold from forming on parts next to plants. The airflow will mitigate the lack of sunlight in full shade to some extent.
As you evaluate your yard, have concrete contractors like Sunny Concrete Services LLC take a look at the areas you're thinking of and see if they can point out potential issues. They may be able to help you find a more appropriate spot.