What do I do next after beating the 6th gym leader what city is next?

Just head to Mt. Coronet entrance on Route 211 and head north. Make sure you have a Pokemon with Rock Smash and Strength. After you get through you should be in Route 216 just keep following the Route till you get to Snowpoint City, where the next gym leader is.

If you have felt the Earthquake in the Canalave Library already then you should head to Lake Valor. There are Magikarp flopping around in the lake. Battle every Grunt and win, then go in the cave. Saturn should be in and I think you battle him, or maybe it is Cyrus. Anyway, then go to Verity Lakefront and help Prof. Rowan and Dawn by defeating Mars. Now go to Celestic City and then Mt. Coronet that way. Don't cross to Eterna, but go up. Follow the path until you are outside and in Route 216. There are a lot of Skiers, Snowboarders, Elite Trainers, and Ace Trainers along this path with Ice-type Pokemon found here, so be careful. Head up to the cabin. Go to the door, but don't go in. Take five steps east, then three south. Use the Dowsing Machine to find the next HM, Rock Climb. Then head up to Route 217. Follow the path until you get to Acuity Lakefront. When you see the rock wall, your friend is at the top and he says that you need the Icicle Badge and the HM Rock Climb to get up there. Head east and you should be in Snowpoint City. This is where the next gym is.