I'm partial to the only beach site on Merchant, which is the NorthEast site. At least two AA'ers have had up close and personal encounters with moose on that site in the last couple of years (me being one of them). But that whole end of Merchant is very shallow and if you want to fish, you'll likely be better off staying further south (spoken by someone who hasn't taken a fishing rod into Algonquin in more than 5 years mind you). 
Big Trout it sounds like you already know where you want to land. 
La Muir: Like you, it's been years since I've been there. I don't remember being particularly in love with the lake or its campsites, but I only vaguely remember where I even camped there. For what it's worth I really like Red Pine Bay if you're thinking about alternatives. 

Big Crow: two of the three sites just to the northeast of the ranger cabin are quite nice. The far north site on the east side of the lake I also remember really liking, although it's been years since I've camped there. 

Proulx: paddled through it at least a dozen times, still haven't camped there. It never manages to work out that way in my trip planning. The southern-facing point site right as you're making the "turn" in Proulx has always looked very nice as I've paddled past it. 
 

Some site specifics for you. The campsites 18-21 on pci map are all good sites. Large, open, (and not a stick of firewood anywhere in September) sites 16 and 17 were very small and on an angle. The island around the corner ( site 22 pci) was more of a fisherman’s camp, it had no fire pit and no seating, but a lovely sandy beach spot on the backside of the island. We spend 1 night on proulx on the way to big crow, and ended up having to take campsite 2 ( pci) which was a dark, dank, difficult to land at site. On the way back we checked campsite 8( pci map) very high site on a sand hill under open pines. You could put an army of tents there, it was so big. A fantastic site!  We stayed at big crow on site 1 ( pci) which had a sandy beach, large site, beautifipul, level. Site 2 was righ5 beside us but difficult to access up a steep hillside. Only other way to get there was through site one. It stayed unoccupied while we were there. Site 9( pci) is another fantastic site with a very long sand beach right around the corner. Site 3 is also a real big, real good, sandy beach site.
Hope it helps!
As for fishing, I can’t help as we don’t fish, but big crow is a very busy lake and many people complained the fishing was not great at least in September.
As for going up to the tower, you have to go right by the cabin, at the time we were there the people in the cabin did not like the constant flow of canoes coming over to them to access the trail up to th3 fire tower.
Have fun!

Swift Fifteen wrote:

Thanks for the tips, guys.  And yeah the PCI is a valuable tool when comparing campsites. Ive used it s lot in the past.

 
I agree that the PCI is valuable and I’ve used it in the past. I wish it was more complete. I also wonder if park staff will eventually put up pics  and ratings of their sites as is now being done for so many Ontario parks.