Almost anywhere in the centre, especially on the Upper Steinweg with its open-air cafes and restaurants.
Nothing like English pubs in Mühlhausen. But try the Antoniusmühle just inside the Frauentor gate. Nice courtyard and family run.
Best cafes are in the Linsenstrasse or the Neue Strasse, where there is a delightful teahouse. If you like cafes Vienna style the best is the longstanding Cafe Schikore in the Erfurter Strasse just off the Untermarkt. You can sit here for hours undisturbed and they have plenty of the latest magazines and newspapers.
Mühlhausen also has some very good ice-cream cafes: the San Marco on the Steinweg, the Al Mulino in the Johannisstrasse just outside the Outer Frauentor gate, and one near the Schwanenteich Lake, a favourite place to walk just on the edge of town.