Ok I finished the game but I continue from the beating savory and dandelion..

After you beat the game, Connie can be found at Seagull Beach - the place where you started the game, and where you first met her.
But she'll only appear there after you talk to certain other NPCs. Not necessarily in order, but here's the order I normally do it:

First, talk to Marjoram. He's in the Bread/Food Shop in Happy Garland. Then go to the Station Hotel ballroom place, and talk to Fennel.

Now head to Eurydika, to the old house where you put Rosemary, Connie's mother, at one point in the story. Now go all the way to Vision Ranch, and talk to Doctor Nutmeg.

Then go to Nefroburg, and check out the alleyway/tunnel things, that lead underneath the rails/tracks - near the exit to Vision Ranch. Finally, go to Miss Echinacea's house - she's Connie's neighbor.

And that's it. Once you talk to all of those people, you can head to Seagull Beach. Connie should be there.

I'd recommend challenging her to a fight/duel. You'll unlock her in 'Battlemode' (which can be accessed from the game's main menu. This is the one time you can unlock her there, and it's the only chance you'll have in the entire game.

She's easy to beat, too. So you don't have to worry about losing. And beating her doesn't lower your relationship standing with her, either.