re: Paris/Barcelona/Rome trip in mid-May...I need some recommendations

+1 on the high end for lunch. This can be an especially great strategy if you are traveling in a country like Italy, where a lunchtime closure (risposto) of shops, tourist attractions, churches, etc is the norm. You don't want to be wandering around just after lunch trying to find something to do when every damn thing is closed up tight until 3 or 4 pm. Go have a nice, long lunch, then a little rest/nap/stroll...