Hello GNS, welcome!
The image quality problems you are having may actually be a result of more than one factor so bear with me.

I'm wondering if you're camera is set to a high ISO value. If so, that would account for a "grainy" appearance under any lighting condition. (This is similar to the grain/ASA relationship of film.)
Regarding your night shots, are they actually "grainy" or "noisy"? There is a difference. "Noise" is an artifact of long exposure times. (Whereas "grain" is generally an ISO-related condition.) Does your camera have a Noise Reduction mode? If so, try that for those night shots.
If you're finding that all of your images are less than sharp (soft focus, rather than blur) then take a look at the sharpness adjustment on your camera. It may be turned off.
Finally, you didn't mention what image quality setting you are using. If you are using JPG Basic, or Normal you would also expect to see pixelly (is that a word?) images. These would look coarse and not too sharp. For printing you would want to use a TIFF, RAW or JPG Fine mode setting.
These are just several of the factors that could result in the type of image problems you mentioned.
Hope this helps.