I think you made a fault with your spellling and games
the gymleader from Saffron is in Olivine city in HeartGold and SoulSilver,
But in Diamond and Pearl Jasmine, the gymleader from Olivine city is in Sunyshore city,
She is on a journey...
The cave is called Dragon Cave and it's situated in a lake behind the city the gym is in.
The 5th Gym Leader inPokémon HeartGold is Chuck, he can be found in Cianwood City.
you have to beat other gym leaders before you can get your hearthome city badge, lol. it's probably the hardest badge to get.
Just go in a straight line on the opposite side of the warp panel you came out of. You will get there :)
The fifth gym leader is fantina.She is in hearthome city.
she is in the light house in olivine city.
Jasmine, the Olivine City Gym Leader, has two Magnemite and a Steelix when you first battle her.
The sixth gym leader,Sabrina, is in Saffron City.
Sabrina, a phsycic type leader
The 14 gym leader in heart gold is in Saffron City.
saffron city (psychic type gym leader)
The cave is called Dragon Cave and it's situated in a lake behind the city the gym is in.
The Johto Gym Leader Jasmine from Olivine City is in Sunyshore City.
Sabrina in saffron city
Sabrini. She is in saffron city.
Olivine City
Jasmine is the Olivine City Gym leader