Is there a point in universe that is observable at present? We know that we can see distant galaxies only billions years before now. We can observe the nearest stars just several years before the present. Something on the Moon can be observed only some seconds in the past. 
Continuing this scale, is there an object in the universe that can be observed just now, at present, or at least closer to the present than any other object?
I suppose such object should be located in the brain of the observer, but where in the brain exactly, given that brain has finite dementions.
The question can be formulated differently: where exactly is located the center of the sphere of the cosmological event horizon for a given observer?
 A: Perception of an event by a brain is a process distributed over a large part of brain's neural network (rather than being a process performed by a single special neuron cell). Thus, for perception to occur a part of the network must reach a state distributed across multiple neuron cells. Due to the limited speed at which neural impulses travel along axons and dendrites and across synapses, there is certain amount of time between the instant when sensory inputs reach the brain and the instant when the neural network settles in a respective distributed state. This means that even the perception of brain's own state isn't instantaneous.
This in turn implies that even "here" isn't perceived "now" and that no point in the universe is observable at precent.
A: An answer in more or less the same spirit as Adam's:
You need to consider the time involved for the neural impulses to get to your brain and for your brain to make sense of the information. Neural impulses travel considerably slower than light, and you'd expect a number of neural impulse "bounces" to take place for any sort of "making sense" to take place.
Putting some rough numbers in, if the impulses go at $100\textrm{ m}/\textrm{s }$and there are (say) ten $10\textrm{ cm}$ bounces, then it takes your brain $0.01\textrm{ s}$ to "see". You might try and push these numbers, but it's unlikely you'll get anything significantly smaller than $100\textrm{ $\mu$s}$ for the response time.
My answer to your question is then, you see "now" anything close enough to your eyeballs that light reaches it within your brain's response time. With the numbers above it's anything inside a sphere of radius $30$ to $3000\textrm{ km}$, i.e. city-size to continent-size.
A: Firstly: Natural science does not encompass the concept of a highlighted instant "now" on the time axis.
Secondly: Considerations on brain size, brain location, and propagation speed of neural signals are not relevant for your question.
You will not be satisfied by these points. Therefore I describe a rat in pure terms of natural science: Suppose it approaches a tube from which emerge attractive odours. Suddenly it receives an electrical shock. A memory trace is formed in its brain so that on the next day it refrains from going there. At the instant of the retrieval of that memory this is a present neuronal process which comes together with further present processes of seeing/smelling the tube so that the behaviour of the rat is different from that of the preceding day. Most importantly, there are no "significances" in natural science. Just as cellular processes running in the kidney, neuronal processes signify nothing (not to be confused with "correlate"). Thus, for a rat, as seen by natural science, there is no past (in a sense that it can be recalled as having happened yesterday), although the neuronal processes depend on time. The rat behaves differently on the two days, but it does not "know" this. Retrieving today even a perfect copy of a neuronal process stored yesterday is no more than running a special present neuronal process. It does not imply that you "know" what it signifies (e.g. an event having happened yesterday, or "time" in general).
The same is true for the human brain. Therefore your question cannot be answered in exclusively natural-science terms. However, being a human, I have consciousness which is subjective and which I experience internally. There is a phenomenal level of consciousness on which I find various phenomenal contents such as time, or an apple, or my entire scientific knowledge, while in my brain there are only well-organised neuronal processes. Most scholars falsely assume that phenomenal contents and neuronal processes progress (quasi-)synchronously on the time axis (which is phenomenal as well). In fact, even simple capacity considerations show that neuronal processes (including memory retrievals) cannot continuously, synchronously and constantly signal my visual perceptions (which are phenomenal contents) of my office, with a wealth of details, all perceived as absolutely constant during many hours. Rather, (scientifically not understood) the phenomenal level operates with prototypes which remain constant by definition. (This is not a physiological memory.) It bears certain similarities to Zip data compression: A collection of prototypes and a "list" of temporal occurrences for each item. Briefly, and somewhat vaguely, this list is our time concept.
There is no scientifically valid statement about the relationship between the neuronal and the phenomenal levels. Therefore one must not say that my phenomenal contents are caused by, nor that they are properties of my neuronal processes. Yet, in a purely descriptive way, I am allowed to consider the phenomenal contents of consciousness as "significances" of my neuronal processes, and an "observation" is an increment of phenomenal contents, somehow brought about via sensory processes. Visually guided lifting of the foot over a kerbstone (not involving consciousness but scientifically understandable) is not an observation. A relationship between the locus of a nervous system and a "locus of an observation" cannot be expressed in scientific terms.
I cannot answer your question. But do you believe that now you can reformulate your question?
