We have done most of our cruises in May, in the Carribbean. It is a great time. The weather is warm, haven't had trouble with rain and there aren't too many kids yet. Not that I am saying not to take your kids, however, I have cruised in July and most of the kids are bad because the parents let them do what ever they want because it is summer vacation and "what can happen on a ship"? We are going to try November this time, but I really like May! Enjoy
Sensation (without KathieLee) July 2001
Paradise (smokefree) March 2002
Valor (inaugural season) May 2005
Truimph May 2007
Fascination (1st time w/DD) May 2008
Pride (with DD & DS) November 2009
The Pacific coastline has the Arctic current flowing down it, so it may be a tad breezy/chilly on deck at night. But, usually only the first and/or last nights. Just take a light sweater and you will be fine. Not much difference between May and summer, since the current comes from very far north.
Late April, May and early June are the best times to cruise, in my opinion, with October and November close behind. May offers the best chance for great weather, there are very few children on the cruise which changes the entire demographic and cruise experience. I have absolutely nothing against children, when I cruise with my daughter and grandchildren, we cruise during the summer months, know what to expect and have a great time also.
I forgot to mention that the weather in ports will probably be a lot nicer in May. We were in Mazatlan once in late July and it got up to 114 degrees!
Plus very high humudity. I don't mind heat too much, but that was just brutal.