Intercostal veins drain into the azygous/hemiazygous veins, which run right next to the vertebral column. Another useful diagram showing left and right intercostal veins.
If you want to think of this simply, the ribs are connected posteriorly to the vertebral column. and the intercostal veins run between them, so they are the closest to the vertebral column.
This image shows the multiple veins which drain breast tissue. easy visual. (to easy to miss it, but i did)
Why is it that the intercostal vein provides the most direct pathway for metastatic breast cancer cells to spread to vertebral column? I thought it was internal thoracic (mammary) and I couldn’t find much searching online, besides wikipedia saying that internal thoracic vein drains the breast.
Goljan mentioned this (not sure what lecture -- might have been the endo one).