Hi, welcome to the wonderful world of cruising! I've done the Mexico Riveria cruise three times, but it's been several years.
First, for things to do in port, check the Carnival website (
www.carnival.com) for shore excursions.
That will give you an idea of what's available.
Puerto Vallarta: There are Jeep tours, dolphin encounters, city tours, booze cruises, snorkeling cruises, just about anything you'd care to do! If you're on a budget, you can just go into town for shopping and people watching. Personally, I usually rent a Jeep right at the dock and take off on my own...I go to a place that takes about an hour to get to (south of town) and is up in the Jungle. Actually, there are two places: Chico's Paradise and Chino's Paradise. They're two spots where rivers come down off the mountains and form cool pools for swimming and jumping off rocks. Both also have restaurants. You can also hire a taxi to take you there, but make sure he stays because it's not always easy getting one back. These spots are pretty easy to find...you go along the coast for awhile (past some very scenic spots), then head inland. Ask anyone for directions.
Restaurants in Puerto Vallarta...well, my favorite thing to do is go up to the El Nido bar which is a rooftop bar atop the Chez Helena Hotel in a residential area of Puerto Vallarta. Best view of the whole place. Since you're traveling with small children (who might want American food!) there is a Hard Rock Cafe in town.
Mazatlan: I've never cared much for Mazatlan. Most people from the ship end up at Senor Frog's (any cab driver can take you there). This is the night where the ship seems strangely empty because so many people are sleeping it off!! It's sort of fun to watch, but if you don't think it appropriate for your kids, check out the excursions on the website. There may be some good ones; I've just never done them. Oh, another thing I've done is taken a cab out to the El Cid Hotel. You can use their beach which is pretty nice.
Cabo San Lucas...all three times I stopped there, the ship was only there between 7 and noon so a couple of times, I didn't even bother getting off. I see you're staying there long enough to actually do something. Sorry I can't recommend anything since I've not really been there! Note, however, that (unless things have changed) the ship doesn't actually dock there...they have to "tender" you in. There are plenty of shopping opportunities right at the pier.
I've done this sailing in late November and had perfect weather. The nice thing about cruising from California in the winter is that you don't usually get that June gloom (cloudy, overcast skies). And it will get warmer and warmer the more south you go. December is actually the high season for that part of Mexico, so it should be very comfortable but you may need a sweater in the evenings.
Packing depends on how casual you are. Carnival ships are the most casual--you can really get away with anything. I've even seen people wear shorts to dinner (although I don't recommend it!). Since you have young kids, you may even want to do the more casual dining route (buffet) if it's more convenient.
If you're like me, you'll overpack no matter what you do, so just give in to it.
I don't have kids, but from what I understand Carnival has a great program for them. You shouldn't have any problem keeping them entertained.
By the way, I was on the Pride 2 years ago and it was one of my favorite ships...not too big, not too small. Their supper Club (David's) is beautiful...get the senior parents to look after the kids one night and have a romantic dinner there! (There's an extra charge, $25 a person I think, but well worth it.)
That's all I can think of off the top of my head! Just keep reading through the various posts and you'll find a wealth of information here!
Good luck and happy first cruise!
-Randy