Katniss’s biggest conflict is character vs. society. Although she struggles against other characters (Haymitch, Snow, Peeta, the other contestants), and with herself, these conflicts arise primarily from her being forced into a subservient role. Her district’s treatment, and the capital’s struggle to maintain power in decadence, is the main conflict.
One of her biggest struggles is defining her relationship with Peeta. She is never sure if she can trust him or if he is "playing" her. She remembers the time that he saved her life as a child by getting her bread, but she is in a winner take all battle to the death that only one person can win.
Katniss struggles with the injustice of the reaping and the inequality of the capitol. The people in the capital live easy lives full of luxury while the people in the districts starve. Katniss struggles to hide her feelings against the capitol. She knows she will need to support of the people and she must convince them to like her. She cannot share how she really feels. She struggles to find a way to defy the capitol within the confines of the game.
Katniss also experiences (at least in flashbacks or in retrospect) conflicts with nature and herself as she tries to deal with the death of her father, the poverty it brings, and the negative impacts that it has on her mother and sister.
Katniss faces external conflicts with both the tributes in the Games and the Capitol. Internally, she struggles with her feelings for both Peeta and Gale and the loss she feels over her father's death.