Faithful to the original games. Great!
The setting of New Vegas is obviously California "after the bombs fell", the same as it was in Fallout 2. The atmosphere of the game also is reminiscent of the earlier games: goofy without being cheesy (unlike Fallout 3).
You are cast into the role of a Courier, who happens to be carrying the wrong package, and you nearly pay the ultimate price for it. Patched up by the doctor of the backwater you find yourself in, you're off to find revenge, among other things.
New Vegas is a very open game, where discovering the world around you is actually more important than completing the main quest. You will again spend a lot of time strolling around the countryside (at a languorous pace), meeting the various factions, furthering their goals or those of their rivals.
New Vegas improves on Fallout 3 by limiting the usefulness of VATS, the left-over of the turn-based nature of the original games. This time you are more vulnerable when VATS is active.
Better than I expected!