DS games should work on your 3DS regardless of region.
Also, allow me to add my own recommendation for the ladies out there.Sweet Fuse: At Your Side
Saki Inafune, niece to legendary game developer Keiji Inafune, can't wait to visit her uncle's new theme park. She's been invited to the opening day ceremonies, and is looking forward to a day of fun and excitement when suddenly Count Hogstein - a villain as corpulent and cliche as he is evil - blows up the Ferris wheel, takes the park management hostage, and declares the beginning of a deadly series of games.
It's an otome game, which means you are also trying to date one of six handsome men trapped with you in the park.
One thing to note specifically about Sweet Fuse, as compared to other otome games, is the pedigree of those involved with the game, and the general feel of the title as opposed to many other games in the genre. Sweet Fuse (amazingly) features Keiji Inafune, who helped contribute to the development, and who actually makes an appearance in the game itself. Also, the character designs were done by Kumiko Suekane, of Ace Attorney fame, and are a very refreshing contrast to the usual type of art found in otome titles. Instead of a brood of very similar looking "pretty boys", Sweet Fuse provides a lot more variety in the types of datable men.
Check it out if you like that sort of thing; trust me, it's worth it.