Both the United States and the European Union have expressed a wish to "deepen" a "constructive" relationship with Venezuela now that Chavez is gone. They obviously want one of OPEC's biggest oil producers to be a friend and not a rival, and for the Americans especially, they didn't appreciate the influence that Chavez had over some of his Latin American neighbors.
Yet, despite his authoritarian leanings, this was not a teetering nation looking to oust a dictator in a revolutionary upheaval. Chavez was genuinely loved my many of his people, and the transition to a new government is likely to be a smooth one. His hand-picked successor is in charge for now and unless the opposition can mount a winning challenge before the election next month, the political situation is unlikely to change dramatically. Considering that an American diplomat was thrown out of the country on the very same day that Chavez died, we wouldn't expect a Nicolas Maduro presidency to be all that eager to play nicer with the United States.
Should the government actually change hands in the next election, or perhaps the one after that, then maybe a new leader might decide to alter Venezuela's course. But not all of Venezuela's people will want to go with him, making a major foreign policy shift difficult. A big of part of Chavez's popularity came precisely because he liked to stick it to the U.S. and its friends. He was a hero to many in Latin America and the Middle East, where no one wants to be seen as a puppet of the Americans. And Chavez went far beyond just giving the cold shoulder.
Chavez's antagonism may have cost the country diplomatic and economic support from the Americans, but it arguably earned even more from places like China, Russia, and Iran. He was pals with Saddam Hussein and Mummar Qaddafi when they were still alive and Mahmoud Ahmadinejad is apparently buying the "suspect illness" theory. It's not hard to make the argument that you can gain just as much in prestige and resources, by being an opponent of the U.S. instead of its friend. (It helps if you have more oil that they do. Even with all the animosity, there was still plenty of trade between the two countries.) The "rogue nations' of the world need to stick together.
Chavez had his enemies, to be sure, both inside and out of Venezuela, but as we've seen even in countries like Libya—where the U.S. played a pivotal role in ousting a hated despot—the loss of a dictator doesn't automatically make everyone friends. Again, oil politics will play a big role in whatever path Venezuela's takes, but there's no need for them to quickly make nice with the U.S. and Europe. Chavez's independence (or the appearance of it) was his greatest asset, and the status quo will likely suit his immediate successor just fine.