First, it's not a sure thing that Yahoo will abandon Groups or Mail, but that does seem possible.
Google Groups may be most similar to Yahoo Groups....but I suspect that, with Google, Photos (including old ones/legacy) wouldn't be integrated the way they are with our Yahoo group...they would have to be moved/sent independently to Flickr...
In any case our admin or someone else with access should try to save current member contact list w/email to Excel or Google version of Excel. That would enable restoring relations that might otherwise be lost.
We might instead consider a blog, perhaps via Wordpress.org (which might be free).