What is the distance from the center of the yoyo to its center of mass

What is the distance from the center of the yoyo to center of mass of wood of which the yoyo is composed? I am trying to determine the moment of inertia of the yoyo. The mass is 0.15 kg.

You are not approaching it the right way.
The centre of mass of the yo you IS AT THE CENTRE.
This must be true due to symmetry.

To find the moment of inertia you need to consider concentric rings of material.
If the yo you had an entirely uniform cross section then these rings would have a mass of
density * 2pi() R * width * dR ( volume of material * density)
and a moment of inertia is density * 2pi() R * width * R*2 dR
( moment of inertia of this ring is mass * R^2)

Now integrate this to find the moment of inertia.

If the cross section is NOT uniform then it is usually only possible to calculate via numeric methods rather than by formula.

A spreadsheet and a table of values for example.
But it must still contain the basic element:-
density * 2pi() R * width * R*2 dR

The only difference is that the width of the yo you at various radii is variable and a table of values would be needed.

Yoyos are symmetrical so the centre and centre of mass are the same.

The moment of inertia is difficult to calculate as it depends on the precise shape (and also the amount of string wound around the centre part which varies as the yoyo rises and falls).