How much does a typical visit to a dermatologists office cost without insurance? How much do skin biopsies cost for cancer detection?

Varies. Typically an exam will cost a few hundred. The skin biopsy plus the pathology fee can range from 200-600. These prices varies from place to place. Call ahead and get prices.
Call and ask... New office visits are around $250. Biopsies are around $200. These vary greatly. So, find a board certified dermatologist and call their office, they should be able to provide that information.