houses in Saffron are guarded by Rocket members, as well as the
local gym and they'll only move after you have cleared Silph Co. of
it's Rocket infestation.
Your 1st two stops should be the lower right
house in the city and the fighting-type Pokémon gym. The house has
the Psychic TM, an extremely powerful psychic attack.
The fighting-type Pokémon gym will give
your Pokémon exp. and 1 of 2 new Pokémon, Hitmonlee or Hitmonchan.
Next you should heal and head to Silph Co.
for a long and confusing battle.