The Hood River [1] area offers two different types of fishing. You can go for trout in several beautiful small mountain lakes, most of which are west and south of the Hood River Valley [2]. Notable among the latter are Wahtum, Rainy, and North Lakes, all about 45 minutes west of town on good gravel roads. Then there is Lost Lake [3], the popularity of which might detract from the quality of the fishing during some seasons. Pick up licenses in any Hood River sports shop.
The other option is fishing the Hood River itself, or the Columbia River. The Hood has good trout fishing, and both have good seasonal steelhead and salmon fishing. The Hood River can be accessed from the county parks covered under Camping [4].
Call the Gorge Fly Shop (201 Oak St., 541/386-6977) for information; this operation can also arrange fly-fishing lessons.
Links:
[1] http://www.moon.com/destinations/oregon/columbia-river-gorge/hood-river
[2] http://www.moon.com/destinations/oregon/columbia-river-gorge/hood-river/sights/the-hood-river-valley
[3] http://www.moon.com/destinations/oregon/columbia-river-gorge/hood-river/sights/lost-lake
[4] http://www.moon.com/destinations/oregon/columbia-river-gorge/hood-river/accommodations/camping