The second clauses you list all refer to different parts of the main clause, resulting in slightly different meaning.
Lets replace the main clause by something simpler, for the sake of analysis:
Lisa pfeift [ein Lied, bei dem Tradition und Moderne sich die Hand geben].
This is a relative sentence. Dem refers to the object, ein Lied, and the relative clause happens to involve a prepositional phrase. We could also have something like
Lisa pfeift [ein Lied, das Max mag].
which is more obviously a relative clause.
The wobei and wo variants are different. Wobei refers to the whole action, or the verb phrase
Lisa pfeift ein Lied, wobei Tradition und Moderne sich die Hand geben.
It is the action of whistling a song that is elaborated. This is the relative form of the dabei Pronominaladverb, and is relative to the whole sentence.
Wo can only used in a local sense*:
Lisa betritt [eine Bibliothek, wo Tradition und Moderne sich die Hand geben].
The second clause elaborates on the location of the object -- the library -- and is also a form of relative clause.
Finally, the dabei version is just a form of coordination. It indicates that two actions happen at the same time, and you could even split it into two sentences:
Lisa pfeift ein Lied. Dabei geben sich Tradition und Moderne die Hand.
These two things may not have to do anything with each other, they just occur in parallel. The dabei pronominal adverb refers to the whole previous sentence and in essence is turning the relative wobei into a full demonstrative pronoun.
In practice, it may be that the variants semantically overlap so much that there is not too much of a difference. Does the café remind you of an Alm which is both modern and traditional, or is the manner in which the café reminds you an Alm both modern and traditional? It might not matter much.
*Unless one speaks a dialect where wo is used as a relative pronoun, but that is absolutely non-standard.