It has nothing to do with current capacity. Nuclear has lost a lot to debates much like this one; however, if we wanted the capacity, nuclear would step up and fill it in at a reasonable price. The same amount of power generated by the alternatives would be astronomically expensive. That's one of the problems that plague the alternatives you've named: either they are far too expensive to use at any kind of large scale, or suitable locations are in thin supply, or power output fluctuates unsuitably with a change in weather, and so on. They just can't compete.
The current research into nuclear is making it even cheaper and safer (thorium, etc); the current research into the alternatives is making them cheap enough to be possible with significant demand.
Wind cannot provide a stable energy source. The advances required in battery technology and so-called "smart grids" are still too far off. You can't power a steel mill on wind power.
Solar is extremely dependent on location and, once again, requires a power infrastructure overhaul.
Geothermal and tidal are still untested.
All of the mentioned experimental technologies will require at the very least 20 years to mature and will bring their own problems as well (geothermal has the tiny little problem that it causes earthquakes).
Most people don't understand that undertaking an energy infrastructure update is something that takes decades and has to be planned thinking about its effects 30 and 40 years from now. And that also means that while you wait for technologies to mature you have to use stopgaps. Right now there is no alternative for nuclear and there likely won't be for 20 years unless nations are willing to invest hundreds of billions in research and upgrades.
True, they aren't everywhere. Maybe some of the power-intensive industry can move to them.
EDIT: Here's Bill Gates explaining why nuclear is not optional: http://www.youtube.com/watch?v=JaF-fq2Zn7I