Close to the sea?

OK, I don't know much about nuclear power plant operation, but I suspect that they get built by the sea to be close to water for cooling (which, of course, needs to be purified first) -- except when there are other, freshwater sources inland, or course. Is that why Fukushima is close to the sea?

Anyway, if that is the case, then why not build it a farther and pump the water. Yeah, it will cost a bit more. But given the alternative potential for problem, which was proven this past week... I suspect it is a small cost to have. As many mentioned already, tsunami is not exactly an Arabic word, is it?