Cerulean cave (the spot where you find mewtwo is the best spot in the whole cave.) Elite Four (I bring my Thyplosion and one other pokemon only. I still beat everybody.) Gym Leaders (I battled Falkner 10 times in 30 minutes
During the main story line I don't have any favorite "grinding" places; I just train in tall grass against wild Pokemon and occasionally against trainers who call me on the Pokegear, but that rarely happens. During the post-game I grind against the Gym Leaders at the Fighting Dojo or against the Elite Four. I don't even bother with wild Pokemon grinding at that point in the games.