Genesis 2:2 says that after the creation days, God rested. But I thought God never gets tired. Doesn't Psalm 121 say he never needs to sleep? Please explain.

The original Hebrew verb, shavat, means "cease, desist, rest." To translate shavat by "rest" is likely to confuse, since it suggests effort, fatigue, and the need to recover.  

To move from linguistics to physics, we say that an object no longer in motion is "at rest." And yet physicists in no way consider such an object to be "resting"!

More can be said. I have recently been studying the works of the first century Jewish historian Josephus. In his colossal history of the Jews, the Antiquities, he writes, "And the seventh day we set apart from labor; it is dedicated to the learning of our customs and laws, we thinking it proper to reflect on them as well as on any [good] thing else, in order to our avoiding of sin" (Antiquities, 16.2.3). In his work Contra Apion (1:22), he explains that on the sabbath [a word related to the word for rest/cease] the Jews were not working, but were praying until evening. In other words, in OT times, the sabbath was not for slovenliness or extra sleep; it was used to become more spiritual, not less spiritual!

Certainly there is a lesson somewhere in there for us!