The ultimate game bag was the old green Bag of Holding from think geek. I own three of them, one for cons, one for game nights, one for work. They’re made out of thick canvas, are spacious, nearly indestructible, and have lots of space on the front flap to put nerdy pins. Unfortunately it appears that they are no longer being made.
A nice dice tray is a good investment. They have dual purpose: they store your dice while in transit, and give you a nice, enclosed area for rolling during the game. I like this one:
It has a nice “dice staging area” around the lip, where you can keep the dice. When you put the lid on, the dice stay put in the staging area and do not rattle around.
If you would like a cheep alternative:
Plenty of rolling space. There’s no staging area, but the tray is large enough to fit your dice bag, and other things like pencils, note cards, etc.. One disadvantage is that the sleeve it comes with is cardboard, and will wear rather quickly in your bag.
If you want something smaller:
This fancy wooden box will hold a single standard dice set. Not much space for rolling though.