What does the first scene of the play reveal about Romeo's behavior in Romeo and Juliet?

This scene reveals that Romeo is a moody, lovesick loner who is not violent. 

We learn a lot about Romeo from the first scene.  Romeo does not involve himself in the fight in the marketplace.  He is above such things.  Romeo is more of a loner. He is currently mooning over Rosaline, but he generally considers himself more of a lover than a fighter. 

After the hullaballoo at the marketplace, Romeo’s mother asks Benvolio...

This scene reveals that Romeo is a moody, lovesick loner who is not violent. 

We learn a lot about Romeo from the first scene.  Romeo does not involve himself in the fight in the marketplace.  He is above such things.  Romeo is more of a loner. He is currently mooning over Rosaline, but he generally considers himself more of a lover than a fighter. 

After the hullaballoo at the marketplace, Romeo’s mother asks Benvolio where he is, and says she is grateful that he wasn’t there.  Romeo’s father wanted to fight, and so did Juliet’s father and her cousin, Tybalt.   Benvolio was there, and tried to “keep the peace.”  Romeo was nowhere to be found.  He seems to spend all of his time wandering around at night or locked up indoors.

LADY MONTAGUE

O, where is Romeo? saw you him to-day?
Right glad I am he was not at this fray.

BENVOLIO

Madam, an hour before the worshipp'd sun
Peer'd forth the golden window of the east,
A troubled mind drave me to walk abroad
Where, underneath the grove of sycamore
That westward rooteth from the city's side,
So early walking did I see your son… (Act 1, Scene 1)

While Romeo is roaming around keeping his own company, he is also not concerning himself with his parents’ feud.  He didn’t try to stop it either, like Benvolio.  Romeo is completely self-centered.

When Romeo sees Benvolio, he tells Lord Montague to leave so he can talk to Romeo alone.  He thinks he will get more out of him without his father there.  What he gets is complaining.  Romeo is complaining about how Rosaline is not interested in him.  Benvolio tries to get him to move on. 

BENVOLIO

Be ruled by me, forget to think of her.

ROMEO

O, teach me how I should forget to think.

BENVOLIO

By giving liberty unto thine eyes;
Examine other beauties. (Act 1, Scene 1) 

Alas, Romeo tells Benvolio “thou canst not teach me to forget.”  He is pining, and he seems to be stuck in his brooding state.  It is a wonder that they ever got him to that party at all, where he met Juliet and finally moved on from Rosaline.