Boy, this brings back memories. From another lifetime, I think. I used to fish around Eureka back when the redwoods were just seedlings, and I don't know if what I remember has any relevance to today's world.
Anyhoo, back in the good old days, as soon as the waves broke over the Eel River bar, usually in late November, after the first really heavy rains, there would be steelhead in the lower Eel. If the river dropped fast and the rains weren't too heavy, the fish would stay in the lower river for a while. If the river were high, the fish would scoot up. However, there were lots of other streams to fish beside the Eel: Redwood Creek, Van Duzen, Mad, and Little rivers, to name a few. Things were pretty crowded on weekends, but the weekdays, particularly on the smaller rivers under low and clear conditions, there was plenty of room to fish.
During the time I fished around there, there was considerable logging activity and the streams muddied up quickly and stayed muddy for quite a while. Things should be better now.
As for flies: simplist thing is to fish Glo-Bugs off a strike indicator. If you don't like that, fish near the bottom with bright, big flies for cloudy water and smaller, drabber flies for clear water. There are fly shops in Eureka that can help. The big trick will be finding fish -- there are lots of places to try. You should have a good and interesting time of it. Keep us posted.
Cheers,
Eric