For the best experience, plan on spending one to two weeks on Vancouver Island. This gives you enough time to road trip from Victoria through Nanaimo and up to Either Tofino and Ucluelet or Bamfield. You can also reach the northern communities like Telegraph Cove or Port Hardy. With two weeks, you can explore both the rugged west coast and the more sheltered east coast, including time for whale watching, hot springs, and hiking.
At minimum, plan on spending 4-5 days on Vancouver Island. This gives you just enough time to explore one region thoroughly. For example, you can focus on Victoria and the southern Gulf Islands, explore the Nanaimo area and central island attractions, or concentrate on the Tofino area and Pacific Rim National Park on the west coast.