Earlier rather than later is the general idea to increase the odds of avoiding excessive fog. May/June appear to offer the best odds, July can be a mixed bag and there's a reason that out there they call it "Fogust".
So late June/early July sounds not too bad. We did it early July in 2006 and didn't have excessive fog, but we also missed a lot of sunshine while all the while Georgia strait was clear and sunny. Nevertheless the Broken Group and much of Barkley Sounds inner shores are not to be missed.
The slog out there can be just that; big westerlies are the norm in the summer months in Juan de Fuca. Personally I'd not plan to use San Juan Hrbour(Port Renfrew) as a stopover, leaving Victoria (or Sooke) pre-dawn and getting to Bamfield in one shot would be our choice (it's what we did last time). There are few good spots in Renfrew and no protection from surge and swell. From the US Neah Bay might be a reasonable jump-off point but you'd be adding some distance.
In Barkley Sound:
I'd recommend Bamfield, charming boardwalks, cottages, two gov't docks (busy) and the walk to Riley's Beach on Deer Passage - worthwhile.
Port Alberni YC has an outstation that's a nice visit - reasonable moorage fees, showers, good shelter and a nice location for exploring the nearby islets by kayak or dinghy.
Lucky Creek, near the mouth of Pipestem Inlet is a neat estuary for dinghies and kayaks too, with a nice little series of falls and swimming holes at the end.
Effingham harbour has some charm, though it's fairly deep in many places, and offers day-trip access to the outer islands if swell conditions permit stopping and exploring there (Clarke, Benson, and a few others)
Uclulet is a good stopover/resupply spot with plenty of moorage, supplies, and - this is not to be missed - breakfast at the bowling alley/arcade. No kidding!! There is also an easy walk to some of the outer beaches. The Canadian Princess fishing lodge (an old steamer) is a nice thing to check out as well.
Of course there are many cosy one-boat nooks scattered around the many islands in the Broken Group as well as popular larger anchorages. It's an area where you needn't share an anchorage if you don't want to.
Can't help you with further up, not yet, but I don't believe you'll be able to 'see your boat while sitting in the hot springs'.. it's a bit of a walk into the springs IIRC.
Anyhow, do be prepared to give up some summer - at the very least you'll have a few "marine cloud" mornings than may burn off midday, or not, but even so this trip is well worth it for the differences compared to sailing/cruising the inside waters.
Don't forget to take pics and post them here afterwards!
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)