The end of Dec does have some issues with traveling in that the weather can be rainey that time of year for Anaheim, and snow in some of the Northern parts.
Since its Christmas Break time for most Schools. For example, Nevada has Dec 21-Jan 7 off for thier two week Christmas break time for this year.
As well as the week between Christmas Day and New Years day is one of the busiest weeks of the whole year at Disneyland.
There are usually inexpensive internal flights on a carrier such as Southwest.com (you can only book direct on thier website) and Jet Blue for as little as $50 one way if you book about 3 months out.
LA to Las Vegas usually has those type of inexpensive flights and better imo than taking the bus that time of year as well as there is not much exciting inbetween the two area. And there are usually inexpensive flights from LA to San Francisco, as well as Sacramento to Las Vegas ect.
The Grand Canyon South rim which is located about a 5 hour drive from Las Vegas is really not a day trip, usually at least an overnight there is suggested.
The inferior West Rim is what is closer to Las Vegas, and not what everyone is thinking about when wanting to visit the Grand Canyon in photos ect.
The 14 day Disneyland pass for Australian Residents is a good value, its usually available for less through Expedia Australia and is a great value right now since Disneyland has just gone up, however the 14 day Ticket through Expedia has not yet, so its still being sold at the old prices making it about the same cost as a 3 day Disneyland Parkhopper ticket.
I would not wait to purchase a 14 day Pass if you are interested in getting one, i dont know if that price is fixed for that kind of pass till the end of the year or not, so you may want to find out that info where you live.
You should also keep in mind for the 14 day Parkhopper they are stating on the Expedia website
>>>>"Disneyland® Resort Park Hopper® Tickets expire 13 days after first use or on January 13, 2013, whichever occurs first">>>>
To get just the Disneyland 14 day Parkhopper on the Expedia Australia website, i had to put in dates before 2013 started on Jan 1. But they do carry through partially into 2013 as stated.
You can do day trips to some of the places you mentioned from Anaheim. However, if you will not have a car, Tour travel times will be longer. Grayline Anaheim, and Starline Tours are the larger Tour Companies that offers tours to the places you have mentioned.
To give you some idea of the times. If you were driving yourself, its about a 45 min drive to Universal Studios from Anaheim. Legoland is about a 1 hour drive. Knotts berry Farms is about a 15 minutes drive from the Disneyland area. And the Art Shuttle service offers a route from the Disneyland area to Knotts and back. The Art Shuttle service also goes from Disneyland to alot of farther away Hotels Multiple times per day for a small fee per person.
Many people from Australia have said on the Anaheim forum they have rented a car to drive themselves around and been fine to do so. Since the places you want to visit may be quite spread out, it is more convenient to have a car to get yourself around. Whether you want to do that or not is up to you.
Angels Stadium is also on the Art Shuttle route and is only about 2 miles from Disneyland. However i dont know what may be offered during that time period. Someone else will likely post with that info for you.
You also may want to consider a visit to Sandiego for at least a few days as well, you can take the train from Anaheim to the San Diego area.
There is Seaworld, the San Diego Zoo, Balboa Park, La Jolla Cove, Midway Ship Museum ect ect, is a lovely city to visit imo.
Here are transportation options from LAX to Anaheim
You can stay directly across from the Disneyland Main Entrance and easily walk to Disneyland in a few minutes. Most of those would be smaller Motels, but some are well rated and convenient for visiting.
There are also a few Hotels in farther walking distance such as Howard Johnsons.........an 11 min walk from the Hotel to the actual turnstiles that go into Disneyland. Has Art Shuttle Service.
Fairfield Inn........ (a Hotel, but with mostly exterior corridors) about an 8 min walk
The Residence Inn Maingate .........which is popular for longer stays since its an extended stay Hotel with full kitchens, large rooms, and free full breakfast as well as some weekly "Social Hours". Free Parking. And is located next to the Anaheim Gardenwalk with alot of good restaurants. Its about a 15 min walk, with Art Shuttle service.
Here is a Map of Hotels in the Disneyland area so you can see where things are located. The Disneyland Main Entrance is off of Harbor Blvd near where it says "East Shuttle Area" on the Map.
If you would like more help finding somewhere to stay, you can let us know your budget per night and what kind of accomodation you are looking for.