I feel like most signature restaurants I went to and even some of the 1 credit TS restaurants had a generic sangria, then a few places like Kouzzina had more creative types. I had a typical red wine with orange type flavors at both Yachtsman and Citricos they were both pretty average glasses of sangria but I love the stuff in all its forms so I was happy to be able to get it.
Red sangria is also on the regular drink menu at all the WDW resort lounges so there's no doubt most if not all Disney-operated restaurants will also serve it.
If you buy a ticket to Hoop de Doo Revue, along with your dinner it will include all the sangria you want (not a really fancy type though)
Most of the Sangrias I have had at WDW are made with red wine and a "Sangria" syrup. Not as good as the real stuff that has sat around awhile with the fruit and brandy or cognac added but it still works. Portabello's had the best we've found but that was several years ago so I don't know what they serve these days.