How to use C1V1=C2V2 How do the units work?
Concentration has units mass over volume; or particles (moles by convention) over volume.

It's fine to use $g/mL$ for concentration in a basic dilution equation.

$C$ is never a mass.

So your second equation has proper units.

If you want mass of aspirin in a given solution with concentration $C$, the mass is given by $m = C\times V$