"Greetings", by definition, should only be at the beginning of a letter. "Wishes", on the other hand, can go at the end :-)
Something I write often is "best wishes from [wherever I'm currently at, if I'm on vacation]" - and such a structure is definitely appropriate at the end of a letter.
That said, Jon is also correct that sometimes mentioning where you are is more appropriate in the beginning of a letter. I think a reasonable distinction is: if the reason you're writing is because you're e.g. on holiday and want to say how things are going, then start off with that. But if you're writing to colleagues about work-related things, and happen to be someplace interesting at the time (say, on holiday, at a conference, etc), you might want add the "best wishes from X" at the end.
Put simply, I'd say it depends on how important it is for them to know where you are to understand the rest of the letter.
As for other terms, "Best regards," is suitable for a variety of situations (it's not nearly as formal as "sincerely" or "yours faithfully", but you also wouldn't use it for your family or close friends), while its shortened version, "Best," is a quick and informal ending. As Drew points out in the comments below, "Regards," is another option - while I personally only use it when I'm trying to be civil to somebody who I don't enjoy writing to, to (most?) others, it's a perfectly good alternative that allows you to use "best regards" for those you appreciate a bit more.
If I don't know the person, I generally go with either "best" or "best regards" the first time around, and then "best" in any subsequent e-mails.