Neckarmüller is the big Tübingen institution: a brewery, restaurant and Biergarten built into the arches below the Eberhardsbrücke, with terraces stepping down to the Neckar. The brewery's own helles, weizen and Kellerpils are excellent; the food is Swabian standards done well (Maultaschen, schnitzel, fried potatoes, big salads).
In summer the terrace is the most enjoyable place in town to eat outside; in winter the wood-panelled inside rooms are warm and busy. It can get noisy when the students are in.