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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.
Before challenging the Elite Four,it is the grass on route 47,behind the waterfall.After beating the game,it is Mt.Silver.The rematches are also useful.