aussies ready to ski!

hi there! Was looking at planning a US ski trip for the family. Hubby is intermediate ++ and kids (6&7) are lower intermediate. We were thinking of then doing LA and Disneyland afterwards so were looking at the Californian ski fields. Where are the best resorts. Obviously a ski resort closer to transit to LA would be great! We want on mountain accomodation and ski in/ out, cos its just too hard to have to worry about lugging skis, kids and other gear too far from accomodation! Im currently being quoted for north star. Was thinking about trying mammoth but have read its a bit old and run down in previous forums. opinions?? Want to self cater too, so a supermarket nearby would be great! All the aussie resorts are ski in/ out and have small supermarkets, which is great for convenience. I welcome all suggestions. Just want to make things as easy as possible!