We based in Villefranche for a week last August. I don't know about July, and Nice stations, but in August every morning a different enormous cruise ship anchored offshore. The tenders arrived about 8 and we often mingled with the tourists from the ships at the Villefranche train and bus stations. The day we returned to Monaco (NOT for a special event, just a regular day!) the bus was simply packed. Another was added right behind it but some people couldn't fit on and the tour people were freaking out that they would miss their last tender back and elbowing their way on and some people got pushed off...however-you can and we did WALK from the stop shortly after Villefranche (forget the name) all the way to the lower harbor in Monaco! Then you hike up (and UP!). It was simply gorgeous, a flat and mostly level footpath hugging the coast- spectacular views. It took us about an hour, but we went very slowly- I think it's a couple miles?
So that way, you could just about skip public transport entirely. You could take the first bus or train of the day to the stop I can't remember (sorry!)Getting back from that stop to Nice might be crowded? But at least it's a suggestion for one way!