Some simple tips for having better control over the mood:
Take control of the ambient light
Too often people just leave the ambient light to the default gray color. This is a huge missed opportunity, since the ambient light has huge influence on the mood.
For day scenes, it works well to make the sun light source have a yellow tint (or whatever color the sun is) and make the ambient light have a blue tint (or whatever the overall color of the sky is). If you have Unity Pro and are making an outdoor scene, you can set the Skylight color in the lightmap settings instead and maybe make the ambient color Black, but if not, then setting the ambient light color generally works well.
For night scenes, the ambient light should be really dark. If you want things to be pitch black where there's no light, just set the ambient to black. However, you can often get better mood by setting it to a really dark color. A very dark blue is good at simulating moon light, but experiment at find out what creates the mood you need.
Always use fog
The fog setting in the Render Settings is also hugely valuable for creating atmosphere. If you think fog is only to be used for foggy scenes then you're wrong! If you enable fog but set the density really low, you can use it to create aerial perspective. Aerial perspective is the effect that for example mountains long away get more and more blueish tinted. However, you're not limited to make it blue. In real life, aerial perspective has different colors as well, and generally is closely related to the color of the sky. So you'd typically use a blue color on mid-day, but an yellow, orange, or red color at sunrise or sunset. This creates tons of mood!
Use multiple colors for lighting
It's often a good idea to use multiple tinted colors to make the scene more interesting and less bland looking. For day-light, an obvious choice is the blue for ambient and yellow for direct light setup, which creates a nice balance between yellow and blue lighting. In indoor scenes it's a good idea to make light from artificial light sources yellow tinted (since most electrical lights are yellowish), while light from windows is blueish (since it mainly comes from the sky). But other combinations than yellow vs. blue can be used as well.