"He was not at my place today."
Translation:Il n'était pas chez moi aujourd'hui.
A couple interrelated reasons; first, you have a spelling error in aujourd'hui. Second, the preposition shouldn't be dans, since that means "in", usually in the sense of "physically inside of" - not "at", at any rate.
Third, the use of the passé composé instead of the imparfait sounds rather odd. I think this image summarizes the problem: the passé composé implies a single event, a single point in time in the past - so in the image you can see it labeling a single point on the timeline - whereas the imparfait suggests an action spread over a period of time in the past, a sort of ongoing action, so it labels a line covering a time span in the past in the image. It's therefore odd to put "to be" in the passé composé, since it implies that "being" is a single action that can happen at a determinable point in time, like throwing a ball.
More importantly, you're translating this waaay too literally. The sentence is using "my place" as an informal way of saying "my house", which is not at all what lieu suggests. Perhaps a better word to translate lieu, rather than "place", would be "location". A geographic area, or a point in space. It carries a much more literal meaning; you wouldn't say "he wasn't at my geographical location today".
When learning a new language, you can't assume it's just a cleverly disguised version of your own. You have to learn the way they do things, and not just translate word for word.