Well, there is certainly lots of different examples of conflict to choose from! Really, this play is full of conflict, both internal and external, so you might want to think about picking one example and analysing it rather than trying to approach the whole play and looking for examples of conflict.
One example of internal conflict that I think is rather interesting is Julius Caesar in Act II scene 2, when Calphurnia is trying to get him to stay at home today and he faces this massive internal conflict of whether to trust in the divination and auguries that he has received and to listen to his wife, or to go because of the pressure of what others will say and think about him if he does not. I like it when Caesar says:
What can be avoided
Whose end is purposed by the mighty gods?
Yet Caesar shall go forth; for these predictions
Are to the world in general as to Caesar.
I think whatever you think about Caesar as a character - good ruler or despot - it is hard to ignore his bravery and his self-belief, that are both admirable characteristics.
Other types of conflict that you will want to analyse are of course the conflict between the conspirators and Caesar, in particular between Brutus and Caesar, and also the conflict within the conspirators themselves. Marc Anthony and the conspirators likewise suffer external conflict. Plenty of examples to choose from!
In Julius Caesar there are a vast range of conflicts presented. They include political conflicts, the conflict between fate and free will, conflicts between the heavens and earth, conflicts in relationships and inner conflict.