As long as you have access to your photos from any computer, then you can download them to the computer you're working on.
But what do you mean by Edit? And which OS will you be using? For example, if you are using Windows and want to do simple cropping, Windows already has Paint installed for free. In Vista and Win 7 the Paint application has more editing options than previous Windows OSes.
For more detailed editing, then the computer you are using at the time will need specific software installed, and that is up to the owners' of the computers you are using.
Mark

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