Well I can tell you that IF the salmon are running when you are in Sitka you can just walk down the shore to the Right from the Tender dock and there is a hatchery with holding pens and fish ladders and everything you would require to be right into it. By donation to the Native Band last time we were there. Walk a bit further into the Park and there were more Salmon in a bigger stream. You will not need to take "A tour" Sidewalks and roadway all the way and marked trails in the park. All flat or pretty close to it.
Now will they be running in July when YOU are there... I don't know. You could try the Chamber of Commerce in Sitka via email I'll bet someone there would know for sure.
Someone from the Hatchery in Juneau told emailed me that I could see them there, and that it would be in full swing in July. Is that the same thing as seeing them run upstream? I don't know what it is like at the Hatchery...
Well there is a bit of river below the hatchery and above too that you can see the fish. The actual run is very visible in the park a 10 mim. walk further on. If they are in the hatchery they will be in the creek. I think you will find the hatchery more interesting but you should see the natural setting. It's really not as much fun though.