A story about my trip to Rome

This happened two years ago when I went to Rome with my friend. We were on holiday (you can to a destination, but you go on holiday). The second day we were visiting the Coliseum when it started raining heavily (keep to the same tense as the rest of the sentence).

We quickly ran for shelter. I arrived at a restaurant (you can go to a restaurant, but you arrive at a restaurant, the to is used to denote where you are going when you set out, the at refers to the point of arrival) in front of the Coliseum, but when I turned around I couldn't see my friend. She was lost in Rome.

So I went back outside the restaurant looking for my friend in the streets around the Coliseum. I didn’t find her and I decided to go back (or return) to the restaurant because my clothes were soaking wet.

When I arrived at the restaurant I sat (sit is present tense, sat is past tense) in a chair near the toilets. Suddenly, someone touched my arm. I turned (past tense again) around quickly and saw my friend. She had arrived at the restaurant one hour ago and she was calmly drinking a cup of coffee. My friend is incredibly carefree (or calm).

Telling a story in Rome

This happened two years ago when I went to Rome with my friend. We were going to holiday. The second day we were visiting the Coliseum when it started to rain a lot.

We ran quickly for someplace where we wouldn't get wet. Then I arrived at a restaurant in front of the Coliseum, but when I turned, I didn’t see my friend. She was getting to lost in Rome.

So I went back outside the restaurant, and I began/started looking for my friend in the street near the Coliseum. I didn’t find to her, and I decided to go back to the restaurant because my clothes were very wet.

When I was arrived at the restaurant, I sat in a chair near of toilets. Suddenly someone touched my arm, and I turned around quickly and saw my friend. She had arrived at the restaurant an hour before and she was calmly drinking a coffee. My friend is incredibly carefree.

 to holiday.  >>  this may be phrased correctly for British English (I'm not sure), but in the U.S. we would say "going on vacation."

She was getting to lost in Rome.  >>> This needs to be corrected, but the choice depends on what you wish to express.  If you want to have the reader visualize your friend in the act of wandering around lost, you might use the participle "getting" or "becoming", but get rid of the "to":  She was becoming lost in Rome.   You might use this stylistically, for instance, as a transition to the next paragraph that tells more about what is going on with your friend (that you were unaware of at the time.)   

But in this case, I think probably what you want to say is "She had become/gotten lost in Rome."  Or, simply, "She was lost in Rome."

near of toilets  >>>  I'm not exactly sure what you mean to say here.   But for a U.S. translation, I am going to guess "I sat in a chair near the restrooms."   With this wording, I would picture you sitting in a chair close to the doors to the restrooms, but not actually inside the women's restroom.