A good spot to watch for whales is from Lime Kiln Point State Park (www.parks.wa.gov [1].) along Haro Strait on the island’s west side; Lime Kiln Point State Park is the only park in the country dedicated exclusively to whale-watching. Sit here long enough on a summer day (it may be quite a while) and you're likely to see killer whales (orcas), and possibly minke and pilot whales, Dall’s porpoises, or harbor porpoises.
Rangers are usually at Lime Kiln Point State Park in the summer and fall and can answer your questions. The small white lighthouse was built in 1914 and has a foghorn that announces its presence frequently. Researchers use the lighthouse to watch for whales and to determine if boats are affecting their behavior.
If there aren't any whales to watch, you can just take in the vistas that stretch to Victoria. No camping is available at the park.
Bald eagles live on the island year-round; look for them between Eagle Cove and Cattle Point on the island’s east side.
Links:
[1] http://www.parks.wa.gov