une is definitely correct.

The main verb of the sentence is ‘aime’.

“prendre une tasse de café” is a “proposition subordonnée infinitive”.

The complement of the verb “aime bien” is the phrase “*prendre __ tasse de café après le déjeuner*”. Since the sentence is not referring to any specific cup of coffee, there should be an indefinite article: “j’aime bien prendre une tasse de café après le déjeuner”. By metonymy, you can also say “j’aime bien prendre un café après le déjeuner”. It’s also possible to treat coffee as a mass noun and say “j’aime bien boire du café après le déjeuner” (the sentence with the verb prendre is not wrong, but it is less idiomatic).

Another way to phrase the same idea is “j’aime bien mon café après le déjeuner”. Using a personal pronoun gives a certain cozy feel to the idea of a cup of coffee.

It is also possible to say “j’aime bien prendre le café après le déjeuner”, but the meaning is slightly different, and the sentence sounds a little off to my ears. Here, what is liked is the activity of “prendre le café”, rather than the drink. You couldn’t say “j’aime bien prendre le café après le déjeuner, ça m’aide à digérer”. But you could say “j’aime bien prendre le café après le déjeuner, les conversations sont intéressantes”, and you might say that even if you were a tea drinker, as “le café” is generalized to mean a social activity.