Mack
I agree with you that Flickr is a great choice. It would be my first choice. However, it seems that there is a lot of work involved in uploading to Flickr. I some times use Picasa. In case you do not know, Picasa is a free application from Google. It will organize the photos on your hard drive. It can do a great job of "general" edits such as changing the light, contrast, cropping photos and such. The edits are all nondestructive. You can remove your edits at any time.
The feature the would be useful to your niece is the "web album" button. Once your niece has organized and done basic edits of her photos, she can select which ones she would like to upload and Picasa will do the rest to the work! The photos are uploaded to her free Picasa Web Album. Once the photos are uploaded, she can decied to keep the album private; and allow only those she sends a link to, to see them. Or she can make the album public and they can be seen by anyone on Google images.
All in all, a great piece of FREE software.