You probably do NOT want to "spin" a neodymium magnet in the base, as this will cause the miniature itself to spin.
Magnets have a N/S pole.
And to float something above them, you need to have the N/S poles on the magnet in the object being floated aligned with the base.
There are novelty pen-holders (and very expensive pen-sets) which "float" the pen above the base using magnets mounted within the pen.
Most of them use a back-stop, which keeps the pen from flying off the mount.
The issue with "Magnetic Levitation" is that for an object to get a stable "lock" on the base, you need to have either a Superconducting Magnet (thus at temperatures of a few dozenÂș to a hundredÂș or so kelvin). Or you need to have some mechanism to control the Eddy Currents in the Magnet:
https://en.wikipedia.org/wiki/Magnetic_levitation
Basically, the best you can do is to "fake" the levitation by installing a stabilization piece, or, spend some time and money getting the electronics to control the balance or the levitated piece. The latter is probably not exactly simple (but not ferociously expensive, either).
MB