How do you get to nasagi city?

There's no such City... Sorry to inform you that.

Isthis city in Pokemon diamond ... Don't think so

That's a city in Japanese... In English, it's Sunnyshore City.

After you've obtained the first 7 badges, go to the lake that's right next to Snowpoint City [Lake Acuity]. Battle the admin there. Now, go to Lake Verity and beat the Admin there [for Dawn/Lukas]. And lastly, go to Lake Valor and watch your rival miserably lose against the admin there. Now, fly to Veilstone City and talk to some guy in front of their HQ in the northeast part of town. He'll drop the Storage Key, giving you access to Team Galactic's Warehouse. Manuever through the warehouse, battling some Grunts/Scientists along the way, until you come across a Galactic Key. Now, get out of the Warehouse and go back to their HQ. Using the Galactic Key, maneuever through their HQ and fight Cyrus. Once you beat him, you'll have to go to his secret, creepy lab place. Battle Mars or whatever his name is, and release the three pokemon. Now that you've done that, fly to Oreburgh City and stock up on these items:
10x Super/Max Repels
30x Dusk Balls
20x Full Restores
10x Revives
1x Escape Rope
^^You can never be too safe. Buy the Dusk Balls in Celestic Town or wherever you like. Also, make sure you have Pokemon in your team know HM03 Surf, HM04 Strength, HM07 Waterfall, and HM08 Rock Climb. Once you've done the above, heal your team [if necessary] and save your game.
Now, go north of Oreburgh onto Route 207 [I think] and go in Mt. Coronet. Start using your repels =] Use surf across the water and use rock climb up the rocks. In this room, try to go as north as you can. Once you've exited, you'll be on 1 out of 2 mountainsides. In the moutainsides, there are 2 caves to choose from, plus 1 cave that you came from. To continue forward, you'll have to go through one of the two caves. Don't worry, the wrong cave will just lead up to a dead end eventually. If you end up in the wrong cave, search around for the right one. There's a small part of Mt. Coronet connecting the two mountainside areas, but you just need to follow that to get to where you need to go... This second mountainside area is much more difficult and people often don't find it until someone tells them about it. Go up and use Rock Climb on the wall TO YOUR LEFT. And just follow that path and go in that cave. From here on-out, just follow the path until you make it to the end. Battle the two grunts, and heal your team [using revives/full restores]. Double battle the two admins with your rival. Once you win, your rival will automatically heal your team up for you. Battle and beat Cyrus. Once you win, and after the short mini-clip, DO NOT MOVE. HEAL UP YOUR TEAM!! Now, save your game! Continue the game once it is night in-game. ...When it's night in the game, continue your game. Battle Dialga and try to get his HP in the red zone and has some status problem, hopefully paralyzed. Start throwing dusk balls at him until you catch him, which really shouldn't be that hard. [Save your Master Ball for Cresselia, which can be caught later in the game. She's a pain to catch, take my word for it.] Afterwards, go to the back of this area to get an item [forgot what it was called] which can be useful for Dialga's sake. Now, go back into Mt. Coronet and use the Escape rope to exit. Fly to Pastoria, heal up, and you now have access to Sunnyshore city.

^^This took me a while to write. Please rate and verify it. Also note that for any mistakes you find in it, I did not use my game as a source or any walkthroughs online because I was too lazy. The game is also big, and I might have mixed up a few parts with totally different parts in the game. For that, I apologize. I copied and pasted that from a question that was very similar to this one. >.< It is not plaigarism, because I originally wrote this myself.

What are you talking about? There is no Nasagi city!

That's Japanese for Sunnyshore. Well, all you need to do is get your Seven Badges, free the Pixies [Azelf, Mespirt and Uxie.], then stop Team Galactic at Spear Pillar. Then you can get to Nasagi City.

It is the Japanese name for Sunyshore City

Thats not a city in Diamond.