Varied Thrush are really tough to find on the south island during June. I wouldn't even bother looking in Victoria (not that there aren't plenty of other good birds there at that time).
They do nest in Pacific Rim, but they aren't the easiset birds to get a look at in June. Go very early (5:00 AM) for your best chance at getting a look at one. You will certainly hear them singing if nothing else.
Try the trail that goes from Florencia Bay to Wickaninish (Nu-Cha-Nulth trail?) (you won't need to walk the whole thing) or the trail to Comber's Beach (an excellent beach too). The road from the Port Alberni to Pacific Rim has many pull offs and side roads. A stop anywhere west of Sutton Pass might get you a look at one, or at least experiencing their song.
Hearing a Varied Thrush singing while one is standing in the deep wet moss of a Sitka Spruce/Western Red Cedar/Western Hemlock forest, is the very essence of coastal BC!
