In the play, Elizabeth has quite a bit to be conflicted about. She faces external conflict of her husband having had an affair with their servant, Abigail Williams. Their affair was something outside of herself that created tension and unhappiness in her life. She had to figure out how to deal with that situation, and how to behave after it was over. It created conflict in her marriage, and a huge rift that was evidenced even months after the affair was over. Another external conflict that she faces is later on in the play when Danforth asks her if her husband committed an affair. Admit to it, and her family's reputation would be ruined; so, she doesn't. Earlier, when Reverend Hale comes to visit their home, he presents an external conflict for her when he questions her beliefs about witchcraft, and about the town's proceedings of late.
Internally, Elizabeth also struggles quite a bit. She feels like she was a bad wife somehow, a cold wife, and that was part of the reason that John turned from her to Abby. She was internally conflicted about her potential role in that entire affair. In act two, we see her struggle with her internal conflict of being angry and bitter over the affair still; she still struggles with forgiveness. That is a very personal, internal struggle that she battles with every day. She was also internally conflicted about what to recommend to her husband at the end of the play when everyone wants her to convince John to confess. She admits that she wants him to live, but also that she wants him to be happy. That is an internal struggle--her selfish desire for him to live life with her, or the more noble route of not lying.
I hope that those thoughts helped; good luck!