Can an adverb as an attribute be positioned in front of the noun it modifies?
In short: no, but .... German not only has a very flexible sentence structure but also puts regularly emphasis on certain parts of a sentence by moving them up front, e.g.:
Ich finde die Frage interessant.
neutral order, I find the question interesting.
Die Frage finde ich interessant.
emphasis, It is the question which I find interesting.
This is where the - incorrect - usage of the device comes from in informal language. You have three options to correct the sentence (as an aside, "Café" is written like that, diacriticals matter):
1. Word Order
As has already been said, "das Café hier" would be correct, as well as "das Café in Mannheim". If you say "in Mannheim [mag ich ] das Café [nicht]" it sounds a little like you dislike "the Café" when you are in Mannheim, otherwise not - and your liking or disliking the Café is perhaps not depending on where you are.
2. Relative Sentence
You can separate the "hier" from the main sentence (which, by that would acquire standard phrasing) by inserting a comma. This changes the Adverb to a sort-of replacement for a Demonstrativpronomen:
Hier, das Café mag ich nicht.
This is demonstrative like pointing your finger somewhere and in spoken language usually accompanied by such a gesture. This also puts emphasis on the "hier" and by extension to where you point at. You don't simply state the fact but point out that you disliking it is the outstanding quality of the Café.
3. Change to an Adjektiv
This last possibility is a bit forced for your purposes, but nevertheless correct: "hier" is an Adverb, but there is a corresponding Adjektiv: "hiesig". It means "[the one]located here" in opposition to "dortig" - "[the one] located there". Adjektive stand in front of the Nomen:
Das hiesige Café mag ich nicht.
You can use such a construction to make sweeping statements:
Die hiesigen Cafés mag ich nicht.
You don't like all the surrounding Cafés - maybe only the ones nearby, maybe all in this district, maybe every one in the whole city or state. This will be a matter of context.