Well, if you have to choose a season, I'd recommend spring or late spring. August is the most crowded period of the year, but I think this is because most people can only afford to take their vacations during the summer, otherwise I can't explain why would you want to take your vacation in Italy, exactly when the weather is extremely hot, it's not eve pleasant, it's a nightmare
Winter is nice too, if you don't mind the snowy roads or blocked highways
It's a risk, although it's not like this has to happen... It all depends on the weather.
As far as Autumn goes.... well, it's been raining cats and dogs over here for days, there are floods, it's cold, autumn is just not a good time for travel!
Now, time of the day... hmm..
Well, I love early mornings, the streets are not that crowded, people are either asleep or at work, so you can roam the streets in peace
At noon, you should know every single store closes, it's a "thing" that surprises many tourists. From noon to 2-3 o'clock in the afternoon, everyone is having lunch, taking a break from work. Streets are empty though, so taking a walk can be quite interesting, especially if you plan on taking photos without too many people blocking your view
At night, that's when the cities come to life
And it makes sense, people go out after their siesta, go out to eat, go out to meet friends, etc. So, at night, the streets are usually crowded.