Romeo can be characterized as brave because throughout Act II.ii, he talks to Juliet from the bottom of her balcony in spite of the fact that the watch or her kinsman could have caught him at any moment.
In Act III, Romeo defends Mercutio's honor by killing Tybalt. That is certainly brave.
Throughout the story, Romeo seems to have a sort of preference for peace. When the truth of the matter is that the Montagues and Capulets are at war, Romeo constantly tries to make sure that fights or frays subside instead of further develop. This is the opposite of Tybalt. In fact, sometimes it takes more bravery to say "no" to fighting than it is to actually perpetuate the fight.
In Act V, Romeo is brave enough to take his own life. This is quite a risk for anyone.
If we define bravery as being ready to face danger without any show of fear, Romeo demonstrates bravery several times in Shakespeare's tragedy Romeo and Juliet. Here are examples of Romeo's bravery:
--In Act I, Scene 5, at the celebration of the Capulets, Romeo is struck by the beauty of Juliet--"Beauty too rich for use, for earth too dear!" (1.5.42)--and he feels that he must meet her. Although he is an intruder in the house of his family's enemy, Romeo bravely moves toward Juliet.
--Despite his being a Montague, the family that is an enemy of the Capulets, and an intruder at the celebration in the home of Lord Capulet, Romeo dares to approach Juliet and touch her. He speaks to her as an object of exalted love, and he bravely dares to ask for a kiss:
My lips, two blushing pilgrims, ready stand
To smooth that rough touch with a tender kiss. (1.5.95-96)
--Later in the night, Romeo bravely risks being seen by the guards as he climbs the Capulets' orchard wall in order to reach the area beneath Juliet's balcony.
--Romeo and Juliet dare to marry each other without their parents' permission or the traditional procedure in which the maiden's father arranges the marriage with the prospective husband. Knowing the danger that they bravely risk, the Nurse tells Juliet that she will "fetch a ladder" (2.5.66) so that Romeo can climb to Juliet's room after they are married. This will be dangerous if Romeo is discovered on the ladder or in Juliet's room.
--In Act III, Romeo bravely attempts to end the quarrel between Tybalt and Mercutio as he tells Tybalt that he loves him, hinting that he now is part of Juliet's family:
Tybalt, the reason that I have to love theeDoth much excuse the appertaining rageTo such a greeting. Villain am I none.Therefore, farewell. I see thou know’st me not. (3.1.34-37)