I enjoyed the Harry Potter series and have found these other titles enjoyable because of the characters' relationships and adventures:
"The Lightning Thief" by Rick Riordan (Book 1 of the "Percy Jackson & the Olympians" series)
"Percy Jackson is a good kid, but he can't seem to focus on his schoolwork or control his temper. And lately, being away at boarding school is only getting worse -- Percy could have sworn his pre-algebra teacher turned into a monster and tried to kill him. When Percy's mom finds out, she knows it's time that he knew the truth about where he came from, and that he go to the one place he'll be safe. She sends Percy to Camp Half-Blood, a summer camp for demigods (on Long Island), where he learns that the father he never knew is Poseidon, God of the Sea. Soon, a mystery unfolds and together with his friends -- one a satyr and the other the demigod daughter of Athena -- Percy sets out on a quest across the United States to reach the gates of the Underworld (located in a recording studio in Hollywood) and prevent a catastrophic war between the gods."-catalog summary
"Sabriel" by Garth Nix
Sabriel, daughter of the necromancer Abhorsen, must journey into the mysterious and magical Old Kingdom to rescue her father from the Land of the Dead. First in a trilogy. The relationships between the characters are well-drawn and bring you back for the rest of the books in the trilogy!
Another author who creates great characters and realistically explores relationships is Peter Dickinson. In "Inside Grandad", Dickinson's evocation of the relationship between Gavin and his grandfather is wonderfully moving. Gavin's grandfather takes care of him while his parents are at work. When Grandad suffers a stroke and is hospitalized, Gavin tries to make a deal with the magical selkies to get his Grandad back.
Graham Joyce uses his fantasy stories to explore relationships and society. I enjoyed "The Limits of Enchantment" for the portrayal of the relationship between Mammy, an old witch who is teaching Fern the secrets of her art. As our catalog notes, the book "...tells the story of two extraordinary women -- one who was born ahead of her time, the other whose coming-of-age coincided with a time of great change. ...
England, 1966: Everything Fern Cullen knows she's learned from Mammy -- and none of it's conventional. Taught midwifery at an early age, Fern becomes Mammy's trusted assistant in a quaint rural village and learns through experience that secrets are precious, passion is dangerous, and people should mind their own business. But when one of Mammy's patients allegedly dies from an induced abortion, the town rallies against her.
As Fern struggles to save Mammy's good name, she finds communion with a bunch of hippies living at a nearby estate...where she uncovers a legacy spotted with magic -- one that transforms her forever."
I hope these are of interest to you! If I can be of further help, please drop me a line.
Mary M. Buck