Hyvä tapa juoda kahvia on mennä hiljaiseen kahvilaan.

Tapa means “way” or “method” and combines directly with an infinitive to mean “a way to do something.”
• tapa juoda kahvia = “a way to drink coffee.”
This entire phrase acts as the subject of the sentence.

After nouns like tapa or following the copula olla (to be), Finnish uses the first infinitive (ending in -a/–ä) to form infinitive clauses.
• mennä = “to go.”
Here you’re stating what the “good way” is, so you need the basic infinitive “to go,” not a finite form like menen or mennään.

The illative case (marked by -AAn on type-I nouns) expresses motion into or toward something—“to a place.”
• kahvila → drop -a, add -aan → kahvilaan
• The adjective hiljainen agrees in case and number → hiljaiseen kahvilaan (“into a quiet café”).

Yes, it’s grammatically possible, but it’s repetitive to use juoda kahvia twice. More natural variants are:
• Hyvä tapa on juoda kahvia hiljaisessa kahvilassa.
• Hyvä tapa juoda kahvia on mennä hiljaiseen kahvilaan.
The original highlights going as the method without repeating “drink coffee.”

Structure here is:
Subject Hyvä tapa juoda kahvia
Copula on
Predicate mennä hiljaiseen kahvilaan
Finnish word order is flexible, so you could also say:
Mennä hiljaiseen kahvilaan on hyvä tapa juoda kahvia.
However, starting with Hyvä tapa clearly introduces your topic and sounds most natural in this case.

Finnish has several infinitives:
1st infinitive: mennä = “to go”
3rd infinitive (illative): menemiseen = “for going” or “in order to go”
Here you simply name the action (“to go”) as the predicate after olla. The 1st infinitive is ideal for that. You would use the 3rd infinitive when you need a noun-like form (e.g., after certain postpositions or to explicitly express purpose).