I have never ridden a bike in Rome, but most of the streets there are cobble stones and the traffic is probably the most unorganised you will find. Other than that, there shouldn't be any problems (except for the heat and the tourists). You should keep your eyes open for less busy, paved sidestreets.
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My advice is free of charge and of respective quality.
1982 Miyata 912
1998 Wheeler 5900 with front and rear air cushion suspension
2015 Canyon Spectral 7.0 EX