Belles rêveries (note the accent) means what google translated: “beautiful daydreams” but is seldom used in French. It has no relation with a good sleep or actual dreams, the latter are rêves while rêveries happens when you are awake.
“Beautiful dreams” translates to (de) beaux rêves and is much more common.
With rêveries, an adjective more used is douces, i.e. douces rêveries meaning “sweet daydreams”.
The translation is indeed “beautiful daydreams.”
A rêverie is a daydream, i.e. when you are awake but don’t pay attention to what’s going on around you because you’re lost in your thoughts.
It does not mean sleeping in the middle of the day (that would be a sieste, i.e. a nap).
But when you say you want it as a tattoo, it sounds like you are looking for the kind of sentence that one could say as a wish to someone else, like when someone goes to sleep and you tell them “sweet dreams” to wish them good sleep.
If that is the case, then for well-wishing, you can’t just use belles rêveries by itself. That just describes beautiful daydreams, it doesn’t sound like a wish to someone. In the case of dreams, the standard way to wish someone sweet dreams is Fais de beaux rêves (literally, “may you have beautiful dreams”); using the same model, you could use:
Fais de belles rêveries — this doesn’t just mean that you want the other person to have beautiful daydreams, it also means that you wish for them to actually daydream more
Que tes rêveries soient belles — this just means that you want the other person to have beautiful daydreams when they do daydream, not necessarily that you wish for them to daydream more.