The quick answer is, specifically, neither. It is not a place but a time-span that is in view.
The phrase in question ζωὴν τοῦ μέλλοντος αἰῶνος (life of the world to come) appears in the Nicene Creed which was agreed upon at the Council of Constantinople in 381. It does not appear in the text of the Nicene Creed agreed upon at the Council of Nicaea in 325.
The Greek word used in the 381 Nicene Creed is αἰῶνος, transliterated as aionos and rendered most often as 'world' or 'age' in English and sometimes as 'ever', 'forever' or 'time'. I was unable to find early church commentary on the intended meaning of this word. My supposition is that the Greek of the NT was so familiar at the time of the writing of the creed that no explanation was necessary. Therefore we must look at how the word is used in the NT, to which the creed refers, to discern the intended meaning.
The word appears 25 times in the Greek NT and is a form of the word αιων (aion) which means life-span, age or epoch:
Our noun appears to describe any length of clearly defined span of time, whether one person's life or some era of certain renown. As general point of referral, this word may also apply to the vast span of history: the ages, the times of old. It's used 126 times in the New Testament - Abarim Publications
The particular form in question is gentitive in form, which usually indicates 'of' and it is masculine in gender and singular in number: of one singular age.
This link to the Englishman's Concordance provides links to all 25 occurrences of αἰῶνος (aionos) in the NT. Looking through the list it appears that what is universally being referred to is an age or period of time rather than a place or realm.
This harmonizes well with Luke 18:30, which not surprisingly contains aion and talks about everlasting life in the "world (age)" to come. Hebrews 2:5 contains the word οἰκουμένη which, though sometimes also rendered world, more properly means just that ... a physical world or empire.
Therefore I think it is safe to say that the phrase * ζωὴν τοῦ μέλλοντος αἰῶνος* (life of the world to come) in the Nicene Creed speaks of an age-during life. That is to say, a life which lasts as long as does the age within which it takes place. If the coming age has no end, then neither does the life within that age: It is eternal life.
The specific place within which this age-during life takes place, be it heaven or earth, is not in view in this last phrase of the Nicene Creed. A faithful English rendering of the last bits of the Nicene Creed might look like this:
we look forward to the resurrection of the dead and life everlasting. Amen
Not surprisingly, this is a pretty orthodox summary of the historic Christian hope. Hope this helps.