What should we visit or see in Rome in just two days?

Hello,
me and my boyfriend are flying to Rome in December just for two days. Could you please recomend us the most interesting places? Thank you!!!
The Vatican, Sistine Chapel (by the way this is one little room in a huge building, I was looking for a little chapel - wrong). The coliseum with all it's cats, Trevi fountain...
By the time you leave your brain will probably be in serious overload. So much to take in in so little time, I was there for 3 days and it left my head spinning. Visually overwhelming.

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