Family of 4 was planning on trip to Italy in late June ( 2021), but now we are open to the idea of going early July instead. I was planning on June because I thought it would be much cooler but have learned the is only a 2 degree average difference between late June and early July. What is the better month to visit Rome and why?
Late June or early July will not make much of a difference. By that time the weather has heated up, and it is definitely tourist season. If you can, I'd go even earlier, such as late May. That's when I visited Rome last summer and although it was starting to get into tourist season, it was not as crowded as it gets in later summer and not as hot (or smelly!). I suppose late June might be better than early July but that will not make much of a difference.
Late June will be prettier because more flowers will be blooming, but a two week difference won't be dramatic no matter when you go.