I would argue that Horatio is the most admirable character in this play because of his intelligence, his honesty, and his loyalty.
In the very first scene, he serves as the voice of reason in a very strange situation. Upon seeing the ghost of his friend, Hamlet's, dead father, Horatio correctly concludes that things are not as straightforward as they seem to be in Denmark, and he determines immediately to bring his friend into the loop. Further, he is brave. He is the only person -- though he is not a sentinel as the others are -- who is courageous enough to speak to the ghost and attempt to engage it. The others are all too frightened.
Later, Hamlet correctly ascertains that Rosencrantz and Guildenstern are in Denmark to spy on him and feed information back to Claudius; they believe they are only doing this because of Claudius's concern for Hamlet's mental health, but they are being used by him nonetheless. Horatio, although he is much closer to Hamlet than they, is never even approached by Claudius for this purpose. This leads me to believe that Claudius understands that Horatio is too smart to be fooled into thinking that Claudius only wants him to spy out of concern. Horatio's loyalty to Hamlet and intelligence likely prevent the king from attempting to use him as he does Rosencrantz and Guildenstern.
In the final scene, we once again see Horatio's staunch loyalty to Hamlet, as he tries to drink from the same poisoned cup that killed Gertrude in order to die alongside his friend. Hamlet insists that he stay alive to tell the story of what happened to him. Even after Hamlet's death, Horatio remains steadfast in his loyalty to and love of his friend, despite his friend's glaring flaws. He truly loved Hamlet and valued his well-being, and the same cannot be said for many other characters in this tragedy.