11-14 May. Anything interesting in the city? (Rome)

Dear members! I'll be in Rome a couple of days - May Protected content
Could you recommend the best way of spending my time in the city? Some gems that should not be missed (apart from obvious ones from guidebooks)?
Would really appreciate your advice!

And if anyone wants to meet a Russian family of two people working in marketing (brand manager and digital manager) interested in broad variety of things from art to science, business or fitness - will be happy to see you!