I can't help with LA because we had a car the whole time.

In San Francisco we have often got the BART from SFO. I'm not too sure how "up" for this you are likely to be after a long flight, but it would certainly be the cheapest way to go. Alternatives are shared shuttles (which my Brother has always done) or taxis. The shared shuttle might not be as cheap as a taxi with 4 people, but you might get discounts for the children.
http://www.bart.gov is the website for the BART. A one way ticket from SFO to Powell (or Montgomery) would be $5.35 each. There are no savings for a return, which I think might have to be the same day anyway? It might just be worth going on google maps and seeing how far from the BART stops the hotel is first.
For a shuttle, try Super Shuttle although I think you will find one way fares are $17, so thats $68 which I think will be more expensive than a taxi.

Vegas is much easier, even more so with you staying at the MGM. Did you know you can check into your hotel at the airport? With your internal flight you will arrive at the domestic terminal, which is where the MGM Grand check in is located (right near the bag reclaim). This will save you a lot of time at the hotel itself, and you will get keys/maps and if your room is ready, you can go straight up there when you arrive. Make sure you ask the check in desk for details on any perks you might have with your room rate, and definitely try and get a strip view (I would add this to the booking prior to travel).
As for how to get to the MGM. Go with a taxi which is located right outside the bag reclaim. It will take 5-10 mins only and will cost $10-$13, round up to $15 for the tip (thats what we do anyway). It really is a very easy transfer, and can I just say...great choice of hotel
BTW don't worry too much if there is a huge queue for the taxis as this will move extremely quickly and you will be near the front before you know it. Its also a good opportunity to get used to the heat of Vegas, if only for a few minutes before you get A/C'd out in the taxi, hotel and room.

Sounds like a great trip, have fun.

Totally agree re Vegas. A taxi is the way to go, especially if there are four of you as a shuttle bus would be $6-7pp one way.

luci

As above cabs in Vegas. And get the BART in SFO it really is so easy and will take you rite into union sq and you will get to see the suburbs out of the window.

stopped at the handerley union Sq twice,first time we stopped had alot smaller room than the room we stopped at last year,if the room not big enough for your family of 4 just ask for a bigger room if posible,there really nice people there an e-mail before you leave may help you,if you use the Bart im sure the station is called powell st you need, takes you to union Sq.walk up 2 blocks where you see cable cars and hotel is just on your left...

We used Suppershuttle from LAX to our hotel in Beuna Park.....there is a website if you wish to check them out...there just outside arrivals when you land on your internal flight from SF..

yep all you need is a taxi when you land at Vegas not far from airport to MGM.