You probably won't find many eagles around in June, but orca tours could prove worthwhile. Most of the boats operate from the northern tip of the island; most are based between Campbell River and Port Hardy.
Closer to Nanaimo, I would recommend Cathedral Grove in MacMillan Provincial Park on your way to Tofino.
Tofino, or, rather, the Pacific Rim National Park, is worth a drive but don't forget to look east as well - too many are caught up on the surf beaches on the western side of the peninsula and completely miss some spectacular scenery to the east.
There are a number of boat-accessible marshes and giant trees groves around Tofino as well. If you do go, I recommend a visit to the restaurant "Shelter".
Another place worth visiting is Strathcona Provincial Park, either through the road to Gold River via Campbell River or Mt. Washington Resort. If you're lucky and inclined to wait, there's a resident herd of elk in the park around the northern shores of Buttle (sp?) Lake. Access is via old logging road. Paradise Meadows, accessible via a short walk from Raven Lodge at the Mt. Washington resort are definitely worth a visit.
North of Nanaimo you'll find the wilder side of the Island with a lot of old logging roads to explore. Pretty much any Prov. Park is worth exploring.
South of Nanaimo is the more settled part with a lot more agricultural and developed land.
There are hundreds of kms of beaches, forests and mountains on the Island. On a clear day you can see the Coast Mountains on the mainland - makes for a pretty picture with a bright moon.
I heartily recommend the +/- one-hour hike (from the parking lot) to the top of Mt. Washington for a sunrise on a clear day. The view is unparalleled.
For a good map and general guide to trails and sights, pick up a "Backroads Mapbook" for Vancouver Island. And enjoy your stay!