Magical Girl Lyrical Nanoha: Anyone can watch this and is an excelent work. Basically, it is about two girls' encounter with one another and their story of becoming friends.
Cardfight Vanguard: It is for everyone. It's more than about a cardgame. It teaches lessons of self-confidence and the art of fair play through the experiences of the main character Aichi.
Tsubasa Resevoir Chronicle: the first and second season were particularly good. It focuses on the love story of the main male and female characters. In addition, the story has adventure, fantasy, and magic. The OVAs you may want to reconsider because they are darker and more serious than either season. However, the movie is for anyone to watch and is really good. The princess of Clow country, Sakura, has lost her memories in the shape of feathers. Her childhood friend Syaoran must travel to different worlds in the hopes of collecting them all. He is not alone, traveling with a swordsman and a wizard each with their own reasons for traveling, along with Sakura herself, he travels to restore his dear friend's memory, but there is a price to be paid.
Cardcaptor Sakura: a classic. It features a little of everything: slice of life, love, action, and magic. The main characters are the same as Tsubasa, but basically a different dimension. A regular girl Sakura Kinomoto one day discovers a strange book in her father's study. She opens it and accidentally unleashes cards of unimaginable power. Now, as a cardcaptor, she must find and reclaim them all.
El Hazard: The Magneficent World: An OVA series. A high school boy discovers a mysterious girl in the ruins of his school. She sends him and three others: his teacher, childhood friend and her brother to the world of El Hazard: the world of endless adventure. It is love story, and has fantasy and comedic elements. However, there is a lesbian, two actually, but the other doesn't appear until later. You'll understand why once you watch the first two episodes. However, it is more for comedy, and nothing really adult happens. If that won't do, try
El Hazard: the Wanderers TV series as that is more simplistic and kid friendly than the OVAs. They are both wonderful stories.
Our Home's Fox Diety: Two brothers are called to their family shrine, and discover they come from a line of water preistesses. The sudden revelation is because the younger brother Tooru is being targeted by a demon. Needing assitance, the matriarch of the family, the grandmother decides to unseal the family's guardian deity, the fox spirit Kuugen. The anime is really a slice of like with elements of the supernatural. The first episode takes care of introductions and the demon incident. Kuugen and a preistesss guardian, a sentinel, in-training Kou comes back with the brothers to their home. From there, many events occur from normal to the supernatural.
Others I haven't watched but know about
:
Emma: a Victorian Romance
Ai Yori Aoshi
Kobato
I'll list more as soon as I can.