I've been looking through Instagrams API trying to figure out exactly how I would show JUST the videos from a certain #hashtag specified in the API call..
If you take a look at the Instagram home page for their blog: http://blog.instagram.com/ This feed for "#WHPmyfavoriteplace" is much like what I want.
You will need to use the /tags/tag-name/media/recent endpoint to retrieve media by tag. There does not appear to be a way to specify what type of media to retrieve yet. You will need to run through your result set and look for media where type => 'video' and ignore where type => 'image'.