If you like The Lightning Thief by Rick Riordan
This readalike is in response to a patron's book-match request. If you would like personalized reading recommendations, fill out the book-match form and a librarian will email suggested titles to you.
And also by Rick Riordan ... The Red Pyramid
After their father's research experiment at the British Museum unleashes the Egyptian god Set, Carter and Sadie Kane embark on a dangerous journey across the globe--a quest which brings them ever closer to the truth about their family, and their links to a secret order that has existed since the time of the pharaohs.
Here are some other titles you might like that are adventurous and surprising:
The City of Ember by Jeanne DuPrau
In the year 241, twelve-year-old Lina trades jobs on Assignment Day to be a Messenger to run to new places in her decaying but beloved city, perhaps even to glimpse Unknown Regions.
The Extraordinary Adventures of Alfred Kropp by Rick Yancey
Through a series of dangerous and violent misadventures, teenage loser Alfred Kropp rescues King Arthur's legendary sword Excalibur from the forces of evil.
Gregor the Overlander by Suzanne Collins
When eleven-year-old Gregor and his two-year-old sister are pulled into a strange underground world, they trigger an epic battle involving men, bats, rats, cockroaches, and spiders while on a quest foretold by ancient prophecy.
Inkheart by Cornelia Funke
Twelve-year-old Meggie learns that her father, who repairs and binds books for a living, can "read" fictional characters to life when one of those characters abducts them and tries to force him into service.
Magyk by Mark Zug
After learning that she is the Princess, Jenna is whisked from her home and carried toward safety by the Extraordinary Wizard, those she always believed were her father and brother, and a young guard known only as Boy 412--pursued by agents of those who killed her mother ten years earlier.
The Mysterious Benedict Society by Trent Lee Stewart
After passing a series of mind-bending tests, four children are selected for a secret mission that requires them to go undercover at the Learning Institute for the Very Enlightened, where the only rule is that there are no rules.
The Night Tourist by Katherine Marsh
After fourteen-year-old classics prodigy Jack Perdu has a near fatal accident he meets Euri, a young ghost who introduces him to New York's Underworld, where those who died in New York reside until they are ready to move on, and Jack vows to find his dead mother there.
Pirate Curse by Kai Meyer
In a place similar to the 1706 Caribbean, two fourteen-year-old "polliwogs"--humans who can walk on water--rely on a mysterious figure known as the Ghost Trader and a band of pirates to help them escape from the evil that is chasing them. (Wave Walkers, book 1)
The Princess Academy by Shannon Hale
While attending a strict academy for potential princesses with the other girls from her mountain village, fourteen-year-old Miri discovers unexpected talents and connections to her homeland.
Quiver by Stephanie Spinner
Greek gods and mortals spring to life in this riveting retelling of the myth of Atalanta, the fleet-footed girl warrior who could outrun any man in ancient Greece. Cast off and abandoned at birth, Atalanta– saved by a she-bear and raised by hunters–proves herself to be a superior archer and the fastest runner in the land. But her skills and independence anger many, including her father, the Arcadian King, who suddenly reclaims her and demands that she produce an heir to the throne. Atalanta has pledged herself to Artemis, goddess of the hunt, who has forbidden her to marry. Unwilling to break her promise, Atalanta suggests a grim compromise: she will marry the first man to beat her in a race, but everyone she defeats must die. All the while, Artemis, Apollo, Aphrodite, Eros, and Zeus himself watch–and interfere–from on high.