Hood River in detail
Greyhound stops at the Mt Hood Railroad station. There are three daily buses to Portland (one hour, from $15).
Amtrak's Empire Builder stops daily at Bingen, on the Washington side of the gorge.
Parking amid all the activity in Hood River can be a challenge, so your best bet is to find one of the close-in public lots and explore on foot. (Bonus: steep hills mean you'll work off your beer.)