Let's say I have an important decision to make and I can't decide between two competing things (like break up with a girl or not break up with her). What would be a word/idiom to express that?
If the reason for lack of a final decision is that you keep switching between the two choices, you can say you're ambivalent.
My favorite word for this is
This implies a person is going back and forth between two or more possible decisions, but can never settle on one. A person who is described this way is by implication a rather flighty individual.
This is similar to Monica Cellio's
waffling. The main difference is that someone who is waffling is by implication a really bad leader. In other words, both words are a bit pejorative, but you are better off to use
dithering for someone whose indecision primarily affects themselves, and
waffling for someone whose indecision primarily affects others.