As others have said, Tofino/Ucluelet are beautiful. With that said, the leg of the trip from Port Alberni to Tofino is very narrow and windy. You wouldn't be the only person towing a trailer to go out there, but it's not high on my list of things to do.
As for timing, if you can push it past Labour Day, there will be a noticeable drop in traffic. However, as Yeti plus said, it will be far from vacant.
Where would I go? I second the recommendation for Victoria and Duncan, and add Cowichan Bay in the Duncan area. Also, the Courtenay/Comox area further north on the East coast of the island are nice. Finally, Cathedral Grove is quite impressive, if massive old-growth trees interest you.
Oh, one last thing - the commuting traffic in the Victoria area is bananas. Avoid being trying to get in or out of there anytime remotely near rush hour.