What is the relationship between Romeo and the Nurse in Romeo and Juliet?

It would be safe to say the Nurse initially likes Romeo very much. They meet in Act II, Scene 4. The Nurse is acting as a messenger for Juliet to discover Romeo's plans for their wedding. After being insulted by Mercutio, the Nurse has a short meeting with Romeo and warns him that he better not be toying with Juliet's affections. She tells Romeo not to lead Juliet "in a fool's paradise." Satisfied that Romeo is sincere, the Nurse says Juliet will be a "joyful woman" after hearing Romeo's news that they should be married that afternoon in Friar Laurence's cell. When she returns to give the news to Juliet in Act II, Scene 5, she is mostly complimentary of Romeo and suggests that he is a very good-looking young man:

Though his face be better than any man’s, yet his leg
excels all men’s, and for a hand and a foot and a
body, though they be not to be talked on, yet they
are past compare. He is not the flower of courtesy,
but I’ll warrant him as gentle as a lamb.

The Nurse is obviously excited for Juliet and simply wishes to see the girl happy. She seems to have not really contemplated the implications of their marriage and is content to help the two young lovers.

The Nurse's fondness for Romeo, however, is disrupted by the news that he has killed Tybalt in the street fight in Act III, Scene 1. When she delivers the news to Juliet in Act III, Scene 3, the Nurse cannot believe Romeo could do such a thing and wishes shame upon him. Juliet, though distraught about the death of her cousin, is happy Romeo has survived and urges the Nurse to find him and bring him to her. Regardless of Juliet's feelings, the Nurse eventually expresses hope that Juliet will forget Romeo and instead heed her father's wishes and marry Count Paris. She tells Juliet in Act III, Scene 5, 

Romeo is banished, and all the world to nothing
That he dares ne’er come back to challenge you,
Or, if he do, it needs must be by stealth.
Then, since the case so stands as now it doth,
I think it best you married with the County.
O, he’s a lovely gentleman!
Romeo’s a dishclout to him.

The Nurse does not realize the depth of Juliet's affection for Romeo. The Nurse seems to believe virtually any man would be able to satisfy Juliet. She thinks Juliet should do the most expedient thing and comply with her father's wishes. The relationship with Romeo has become too complicated.