I would like to know if there are any user located near me geographically. Is there a way to view users by city/country?
You can use the Data Explorer for this. The data is updated fairly regularly. (It's supposed to be monthly, but as of the posting of this answer, the last update was on June 27, 2012.)
Here is an example query I made for you, which you could modify to your liking.
This, of course, only shows users that actually provide a location in their profiles and it may not be accurate since it is self-reported and not authenticated.
Using the Stack Exchange data API, a user created an online map, StackMaps, that takes the information from the user self supplied location and places them on a world map. One can then pan, zoom and select the balloons to see particular users at any location.
Caveat Emptor, when using such a map one needs not be only aware that users locations are self-supplied (and hence may be false), one needs to be aware that the process of geocoding is not guaranteed to produce reliable results. Now, I will start by saying I'm sure I couldn't do any better, but given all the grief Apple has been given over their recent maps, I figured poking fun at google is not entirely out of place.
As cardinal mentioned in the comments, parsing of only country names seems to be alittle out of place, as you can see here a user from Russia is assigned to the northern parts of Quebec.
All of the points that far north in North America appear to be either misplaced or just generally not useful (a few who put Canada were geocoded to what I am guessing is the centroid of Canada in the UTM projection, another who listed the North Pole is given a location in Alaska).
If you zoom in to the balloon in Alaska you will see there is a place actually called the North Pole, and in this instance the geocoding engine was likely alittle too liberal in actually assigning that point. Another example can be found that the Kingdom of Zhao is somewhere in rural upstate NY between Albany and Syracuse (if you zoom in you will see that there is a Kingdom road it is assigned to).
Last but not least, we have some sea-faring posters. I assume Michelle is located at a New New Zealand that I was not previously aware of. You can also see one indvidual who put Chile as their location was placed in the Pacific, I wonder offhand if this is a projection messup/centroid out of the polygon snafu.