Eat

Augustiner Biergarten 
One of Stuttgart's largest beer gardens, where you can naturally eat as well as drink. Recommended by a former work colleague of mine, Stuttgart resident Andreas. Located in a large park, the Kurpark, about 30 minutes' walk from the stadium. For a somewhat posher meal, you could also try the adjacent Kursaal Restaurant, operated by the same people. As both websites linked to here are in German only here's the Kursall Restaurant Tripadvisor page in English and here's the Augustiner Biergarten Tripadvisor page.

Sushi Le 
Another tip from my friend Andreas in Stuttgart. Evidently very much the place to go if you like Japanese food. The company has two restaurants in Stuttgart. The one that Andreas particularly recommends for fans in the city for the Euros is in Bad Canstatt (across the street from The Corner - see below) and thus just under 30 minutes' walk from the stadium. As the website linked to above is in German only, here's the Sushi Le Tripadvisor page in English.

Steffi, another former work colleague based in Stuttgart, and some of her friends suggest the following six places:

Alaturka 
Eat-in donner restaurant, whose kebabs have been voted the best in Germany. Reviews here in English on the Alaturka Tripadvisor page.

Stäffele 
As the website says, a "traditional Swabian restaurant in the heart of Stuttgart". Established for over 50 years..

Ochsn Willi 
Offering 'top Argentinian beef and house speciliaties'. Reviews in English here on the Ochs'n Willi Tripadvisor page.

Brauhaus Schönbuch 
Modern 'beer hall' with over 500 seats inside and out at its city-centre location (there are two others out of town). More photos and reviews in English here on the Brauhaus Schönbuch Tripadvisor page.

Breitengrad 17 Stuttgart  
Vietnamese food. Photos and reviews, including some in English, here on the Breitengrad 17 The Fork page.

Carls Brauhaus
Large bar/restaurant opened in 2014 on the site where Carl Dinkelaker founded the Dinkelalker brewery in 1888. Right in the centre of the city, adjacent to the large Schlossplatz public square.

Drink

The Corner  
As per the beer garden and Japanese restaurant above, another place recommended by Andreas. A corner pub, as the name suggests, which their website describes as being for some the "gateway to hell" and for others what is "probably the best corner pub in the world". The decor gives away a strong VfB Stuttgart connection - which is not surprising as you can walk from here to the stadium in under 30 minutes. As the website linked to above is in German only, here's The Corner listing on Google, where you'll find reviews in English.

Steffi and friends suggest giving these four places a try:

Palast der Republik  
They say it's actually just an old public toilet building, in which there is now a small bar, primarily serving people sat outside. Apparently where many people meet in summer for a few beers before hitting the town. Also plenty of places in the vicinity to grab a bite to eat (e.g.,. Peter Pane, Tobi's). Palast der Republik UK Tripadvisor page here.

O'Reilly's Irish Pub 
You can probably guess what to expect here.

Oblomow 
A classic of a bar say Steffi & co., which stays open until at least 5am. Centrally located. Various reviews here.

Kraftpaule
A craft beer bar with 12 beers on draught. Not far from the main station. Reviews in English here on the Kraftpaule Tripadvisor page.

And if the weather's good, Steff and co. suggest these beer gardens (in addition to the Augustiner one already mentioned above):

Flora & Fauna
Facing out onto parland, this beer garden is situated where the Shlossgarten meets Rosensteinpark. You could stroll there half-an-hour or so through the park. Google reviews in English here.

Biergarten im Schlossgarten
If you want to spare yourself the walk from the main station, you'll find this beer garden almost directly outside it - yet also facing out onto the greenery of the Schlossgarten park. More about it in English here on the Biergarten im Schlossgarten Tripadvisor page.

Karlshöhe
Beer garden overlooking the vale of the city and surrounding vineyards. From the main station: two stops on the S-Bahn and then a 10-minute walk. More photos and reviews in English can be found on the Karlshöhe Biergaarten page on Tripadvisor.