You would use "between" no matter how many nouns are used in the sentence because in this case the word "between" has a different meaning and is used to say that you are making a choice, or cannot make a choice.

"Among" is used to say that something, or someone is surrounded by another thing, for example: "I am among the animals" so you would not say "I can't make my mind up among Rome, Paris and London."

"Between" can also be used to explain that something is done together.

- "A conversation between two people"

As well as the position or time that separates things:

- "I will meet you between 3 and 4 o'clock."

- "I will meet you between shop A and shop B."

And also the combination of something (both effort and object:

- "We have 3 bags between us."

BETWEEN - AMONG

I read this sentence: "I can't make up my mind between Rome, Paris and London". Why "between" is used? There are three of them! I know that with 2 two nouns we have to use BETWEEN and for more than 2 nouns we have to use AMONG is used.

Thank you

The sentence is wrong.  You are correct.  However, consider the following sentence,

"I can't make up my mind between Rome, Paris and London in Europe and Tokyo, Bejing and Hong Kong in Asia."

Here, even though there are more than three involved, the meaning is a choice between two continents.  The example you had given involves more than two choices.