cerulean city.good day sir
This can actually happen. For example your playing Pokemon yellow and you only have pikachu as a Pokemon, you will not be able to beat brock not matter what level pikachu is, but misty can be defeated because pikachu's electric type moves are strong against water type Pokemon.
You can go and challenge other Gym Leaders in the Kanto region, such as Brock.
I know Brock, and probally Misty. Possibly Giovanni
In the grassy area which is after the town where you beat Brock.
You can catch a grass type Pokemon but catching mankey is the easiest because it appears a lot especially to the east of Pewter (where Brock is). Mankey has the advantage of being a fighting Pokemon which is super-effective against Brock's Pokemon.
I don't have heart gold but its Vermilloin city next gym leader is Lt.Surge he has electric Pokemon No,Brock is next,ok?
i say you should look in viridian forest
after you beat the elite four, you can go to to the Kanto region. (at least i think its Kanto its the one with Brock and misty) at the first city, pewter town, there is a man next to the Pokemon center after you beat Brock he will give you the silver wing (gold version) or the rainbow wing (silver version).
meet him and beat him
After you've beaten Brock go beat the other six leaders then you can fight Blue
route 25
Some options that could beat Misty's last Pokemon would be either the Razor Leaf, Vine Whip or Solar Beam attacks.