he is training deep in the cave between ecruteak city and mahogany town. you go past it, and its a pretty huge cave, its a hell of a job finding him, but you get a pretty sweet Pokemon when you beat him ;)
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you can get it if you defeat the fighting gym leader in saffron city but you can only get 1
beat everyone in silph.co and you can get into the saffron gym
He's in Mt. Mortar
There really isn't anywhere is Saffron to "train" but if you go to the left of the city and go through the building with the cop there is patches of grass you can practice with your Pokemon ok the wild Pokemon that thrive there...then when your done..you can just go back and challenge the gym leader of Saffron..the leader is Sabrina: Master of Phsycic Pokemon.
you have to go too Fushia City beat the gym leader then they will let you in Saffron City then go in to Silph Co. and get to the last floor find Giovanni battle Giovanni then then get out of Silph Co. and you can go in the Saffron gym.