I live a mile away from a 10.8 mile, 4072 foot climb. And I visit the gym a few times a week. And in my neighborhood there are a lot of lesser climbs (100 to 400 feet).
Hill repeats can help; they'll build strength in your legs, and cardio fitness.
Stairmaster helps with cardio, but not as much with leg strength as applicable to riding. But for cardio I'm able to hit and hold those heart rate targets on a stair climber just as effectively as on a bike.
Base miles help for leg strength as applicable to riding.
Actually doing the climbs is the best, unfortunately. That 11 mile climb near my house is rough, particularly at the beginning of the season (I don't ride through the winter -- I'm not cut out for riding in the snow).