Is the universe bounded? As I understand it nobody can pinpoint an objective "center" of the universe nor "where" the Big Bang happened. It seems the observable universe is limited by our event horizon at some 14 billion light years and my question is simply: If an astronomer was placed at one of the outermost visible objects would he be looking at a nearly dark sky in a direction away from earth but a star filled sky in the direction of the earth or would he see a more or less evenly lit sky as on earth? If the latter is most likely does it not imply an infinite/unbounded universe?
 A: 
"It seems the observable universe is limited by our event horizon at some 14 billion light years"

The farthest objects whose light reaches us today are some 46 billion lightyears away (the particle horizon). The event horizon only tells us the maximum distance from where light that is emitted today will be able to reach us in the infinite future. But the term "observable universe" is reserved for everything inside the particle horizon.

"If an astronomer was placed at one of the outermost visible objects would he be looking at a nearly dark sky in a direction away from
  earth but a star filled sky in the direction of the earth or would he
  see a more or less evenly lit sky as on earth?"

We assume that the universe is homogenous and isotropic, so it should roughly look the same from everywhere.

"If the latter is most likely does it not imply an infinite/unbounded universe?"

That is what we are assuming when we say "the universe is flat", "the curvature is zero" or "the total energy density equals the critical density".
A: We do know 'where' the big bang happened. It happened everywhere.
Imagine you are inside a big inflated balloon. Now ask where that balloon inflated from. The answer is, it inflated from everywhere.
A: The astronomer would see mostly what we see. That does not mean that the universe is unbounded, it just means that the universe is much, much larger than the observable universe -- which is indeed a consequence of current cosmologies which contain cosmic inflation; in these the universe goes rapidly from being in thermal contact (where it comes into equilibrium, this being why the cosmic microwave background is so darn homogeneous) to being thermally disconnected (which is our present experience of the universe) by the rapid expansion of space. So just because she is at the boundary of our observable universe, it does not mean that she is at the boundary of all space.
A: As the CuriousOne commented, the idea of the Big Bang is that it happened everywhere.  It was not an explosion from one point in a spatial coordinate system at t=0, the spatial coordinates just started expanding (straining by the factor a(t)).  Therefore all space points in our universe have similar histories in time.  What we see now in the light from 13.8 billion years ago is what we would have had around us, right here, 13.8 billion years ago.  When we see light from the CMBR plasma 13.8 billion years ago, then right here 13.8 billion years ago we would be immersed in plasma.
"If an astronomer was placed at one of the outermost visible objects", he would see a similar evolution in time of the sky as an astronomer on Earth ... for which never "would he be looking at a nearly dark sky in (any) direction".  Likewise,  the sky for the hypothetical future of a distant astronomer will look similar to the sky from Earth at the same hypothetical future time (corrected for the light travel time between the astronomer and Earth).  
A: 
Is the universe bounded?

Nobody knows. We have no evidence to say it is, and we have no evidence to say it isn't.  

As I understand it nobody can pinpoint an objective "center" of the universe

Correct. To pinpoint the centre of the universe, you'd have to be locate some kind of edge, and nobody can.  

nor "where" the Big Bang happened. 

It's thought to have happened everywhere, in that space has been expanding for 13.8 billion years. When you wind the timeline back, you get to the point where the whole universe was "the size of a grapefruit". The moot point is that the Big Bang didn't go bang within the universe. It was the whole universe that went bang and started expanding.  

It seems the observable universe is limited by our event horizon at some 14 billion light years

Like Simon (=Симон) said, the particle horizon is 46 billion years away. That's because the expansion of the universe over nearly 14 billion years has resulted in something akin to "compound interest". 

If an astronomer was placed at one of the outermost visible objects would he be looking at a nearly dark sky in a direction away from earth but a star filled sky in the direction of the earth or would he see a more or less evenly lit sky as on earth?

Nobody knows. The distant observer 46 billion light years away might see an evenly-lit sky, or he might see half the the sky as black, or a mirror-image of the other, or something else. You cannot make some assumption that the universe is homogeneous and isotropic and then declare that it must therefore look the same to that distant observer. It just isn't scientific to make such claims. 

If the latter is most likely does it not imply an infinite/unbounded universe?

Nobody knows. If the distant observer 46 billion light years away did see an evenly-lit sky, some other distant observer another 46 billion light-years away might see half the sky as black, or a mirror-image of the other, or something else. 
Note that a cargo-cult canard has arisen since WMAP in 2013 that says "the universe is flat therefore it must be infinite". This is a non-sequitur. It just doesn't follow, and it leads to the indefensible claim that the universe has always been infinite, even at the time of the Big Bang. The claim that the universe is much much larger than the observable universe is similarly unjustified. In olden days it is said that people could not conceive of a world that was curved, and could not conceive of a world without an edge. Nowadays we have cosmologists who can not conceive of a world that is not curved, and  cannot conceive of a world with an edge. It's like we live in a forest, surrounded by trees. And some dendrologists will declare with overweening authority that their assumption of a homogeneous and isotropic forest means everybody everywhere will see trees all round, and that the forest goes on forever. But they can't be sure of that. It just isn't scientific to make such claims. That forest might have an edge. And so might the universe. 
