How do I know where to put stitching vias?
If you flip C2 and C3 around this could be a 1-layer board. Flipping them, would also reduce parasitic inductances due to the required vias. 

But, to answer your question, for your (low-frequency) application, stitching vias serve just one purpose, to reduce the impedance for any current traveling on the planes. That directly implies that areas of the plane that have little or no current, due to being far from the current paths, don’t require any vias. 

In your case you only have 4 pads and a pin that conduct current from the plane. You just require vias near those pads and perhaps the pin (vias are much less conductive than the pin itself). Perhaps 4 vias on the capacitors, and 2 near the IC Gnd.

Any additional vias would mostly be cosmetic, it would be hard to tease apart the effects due to reduction in impedance due to the vias from the increase in impedance due to the added holes in the planes. 

If this was a high-frequency a application (e.g., >500MHz) vias would be required near the PCB edges, to avoid unintended emissions and you would need to take into account the impedances to the plane underneath signal lines.