Let's start with the current protagonist of the entire franchise, Hershel Layton. Layton was intended to essentially be a few-flawed Phoenix Wright. Through the light British accent, the heavily calm demeanor in almost any situation, and being a fencer/sword-fighter/time-traveler/guardian/archaeologist/townsaver/soon-to-be-savior of the world, they certainly hit the nail on the head. Very rarely is he ever at a disadvantage, and he often figures out the truth behind mysteries before any of the other characters do or even the players do, in a way very similar to Phoenix himself (Not to mention the epic fingerpoints of epicness). He also seems to have the ability to make any contraption out of any materials at the plot's convenience, such as a made-from-scratch peddling helicopter, so that's awesome, too. Despite being more or less flawless, though, Layton actually goes through quite a bit of development throughout the franchise, one of the most noteable bits of development being the loss of his childhood friend which lead him to take up a career in archaeology. He CAN grow worried and concerned when situations grow outside of his control, and he has certainly been held down quite a few times in the past.
Luke Triton possesses the child-like attitude we've seen many-a-time in fictional media. Luke acts as the apprentice (#1) to the Professor, acting more-or-less as the Professor's #1 fan. His goal in life is to become a true gentleman and follow in his mentor's footsteps. Despite wanting to be a gentleman with learning to solve puzzles and selflessly helping others in need, he still possesses a child-like arrogance and love of childish fun that often portrays him as being otherwise.
... Not to mention he likes soft, fluffy things. And if that isn't enough, watch this:
http://www.youtube.com/watch?v=NfBEqJZjM1c
Flora, overall, is just so, SO gorgeous. She has a soft voice and a modest physique, along with a nice anime-esque art style, and the gentle, kind-hearted rich girl demeanor that make her a character very easy on the eyes. Her moments throughout the franchise have given her many an adorable moment and she is DEFINITELY an underrated character, even if she is still technically positively received. She's a gorgeous character and extremely loveable, and I'm glad they made her happen.
(She's so underarted, I'm so sorry. <<; )
Cookie... is more of an interesting case. She's a side character in the game Miracle Mask, and overall is very, VERY unimportant to the plot of the game itself. Her point in the game is essentially just to act as a sort of damsel-in-distress for Luke, as her mother constantly loses track of her. The very first time you meet her, she talks to Luke with a very informal tone, choosing to call him "Shorty", despite being noticeably shorter than him herself. Upon him offering to help her return to her Mother, and doing so, she retracts her informal treatment of him and calls him her hero, leaving with an adorable giggle. She gets lost several other times, and throughout, her reactions toward Luke continue to vary, ranging from calling him by his name, Hero, and even Lukie-poo.
... So essentially, her adorableness come from her tough attitude, big, eye-covering hat, and crush on Luke. I promise she's cuter in the game.