Truly the closest river that would hold salmon would be the Eagle River near 3 Valley Gap. But there aren't any salmon in there until October when the Sockeye run. Oh ya by the way it's also closed off for fishing.
The best thing for you to do would be to drive all the way to either Smithers 16 hours and fish the Bukley or the Skeena River. I would recommend getting a guide there. You can check on the internet and find some great places to stay and fish. Here's one place you might want to try. http://www.tworiverslodge.ca/
Or you can go the 12 hours to Vancouver and fish the Vedder or the Frazer Rivers. I would also suggest getting a guide there as well. Check with Freds Custom Tackle on Vedder Road. http://www.fredscustomtackle.com/
Or STS Guiding. http://www.guidebc.com/
Good luck with your adventure.