There's nothing wrong with phrases like "after a moment". Just be careful not to overuse them.
If you find yourself writing:
Al entered the room. After a moment, Sally entered also. A moment later, Al said, "Oh, Sally, it's you." Sally paused for a moment ...
Using the same word or phrase (other than an article, pronoun, or short preposition) repeatedly in a short space tends to look awkward.
As John Landsberg says, in some cases you could replace the "after a moment" with some action. In other cases you could simply omit it. I'd say that the only time you should include it is when you intend to convey that nothing happened in that moment, that everyone was just waiting or standing dumbly.
Bob picked up the book and opened to where he had left off. After a little while, he put it back down.
The "after a little while" contributes nothing. Indeed it leaves the statement ambiguous. Is the intent that he was reading for a little while, that he just stood staring blankly at the pages, that he was thinking about something else, or what? Better to say what he did than just say that time passed.
On the other hand:
Cathy burst into the room and announced to her family, "I've decided to marry Bob!" She was met with total silence. After a moment, her father said slowly, "I suppose the wedding will have to wait until Bob gets out of prison ..."
Here, the idea that everyone stands around saying nothing for a little while contributes to the mood.