There are different viewpoints regarding this matter amongst Quranic commentators:
A number of them believe that Prophet Adam's heaven was simply a beautiful and thriving garden on earth.
Some, unlike the first group perceive that it was in the seventh heaven, the reason being that it is said that Adam “descended” from the heaven when he was asked to leave.
Another theory is that Prophet Adam's heaven was the same promised heaven that we all know about.
The fourth theory says that Adam's heaven was neither the eternal heaven nor a garden on earth, but rather a heaven in barzakh, between this world and the hereafter, and we believe that this theory is what hadiths and the Quran tell us.
The Quran says: «و قلنا یا آدم اسکن انت و زوجک الجنة».
Jannah (جنت) means thriving garden, recreation area, paradise, heaven. And «جنات عدن», which has been mentioned in the Quran, means an everlasting residence and since gardens are usually covered with trees, it is called “جنة”.
Regarding what heaven is, it has been said that it is the most perfect world imaginable, a place with the perfect weather and every sort of blessing for the righteous who have passed away who will reside eternally reside there.
There's a debate amongst Quranic interpreters pertaining to the heaven Prophet Adam was in, the heaven in which he was deceived by Shaytan and as a result driven out of.
Some believe that this heaven was a worldly garden just like other gardens on earth. A few of their reasons are as follows.
1. If Prophet Adam was actually in the heaven of hereafter, it would therefore have never ended and if Adam was in the eternal heaven Shaytan could never have deceived him for there are no temptations there.
2. Whoever enters that heaven never leaves for God Almighty says: "و ما هم منها به مخرجین" "and they are never dismissed from it".
3. When Shaytan refused to prostrate before Adam, he was cursed by Allah making his entry to paradise obviously out of the question.
4. Prophet Adam was without doubt created on earth and nowhere has it been mentioned that he was transferred to the sky in order to enter the supreme heaven.
Some of the ahadith from the Ahlul-Bayt (A.S.) imply and in some cases, directly verify this issue. One example is the hadith in which Imam Sadeq (as) was asked about Prophet Adam's heaven, where he replied: جنة من جنان الدنیا» «یطلع فیها الشمس و القمر و لو کان من جنان الآخرة ما خرج منها ابدا, "It was a garden among the gardens in this world where the sun and moon would rise upon it, and if it were the heaven of the hereafter he would never have left".
Other interpreters perceive that Prophet Adam's heaven was the heaven of the hereafter. The reason why they believe so is that the "ال" (alef wa lam) in "الجنه" can not imply that any heaven and garden is meant (alef wa lam esteghragh), for it is not practical to reside in all the heavens at once, hence the "ال" has to hint at the promised heaven, the one that is well known between Muslims, the rewarded heaven.
The apparent meaning of Imam Ali's saying in Nahj ul-Balagheh: «فاغتره عدوه نفاسة علیه بدار المقام و مرافقة الابرار» confirms this notion.
"But finally -out of the sheer jealousy of him residing among the righteous, in the eternal residence- Shaytan deceived him.”
The “eternal residence” in which Adam resided was Dar ul Khold, where believers stay forever for it is the supreme paradise and it is the place where all the righteous are.
Subsequently Imam Ali also says: «و وعده المرد الی جنته » "And God promised to return him to heaven". This statement implies that God almighty ultimately, sent Prophet Adam back to where he initially was, whereas the only place Prophet Adam would have gone after that was the heaven of the hereafter.
The other viewpoint regarding this matter is that Prophet Adam resided in a heaven located in the seventh sky. The reason behind this theory is what God has said: «اهبطوا منها» "we said descend from here". So the first descent was from the seventh sky to the first sky and the second descent was from the first sky down to Earth.
Another theory that would be considered as the fourth theory seems to be the most reasonable of all, due to the fact that it has tried to take into consideration every relevant ayah and hadith and bring about harmony between all of them. The theory is that: 1- The Alef ((الف and lam (لام) in «الجنة» causes the word jannah to refer to a specific garden known to the reader, rather than being alef lam jens or esteghrag that don’t have this function. 2- That which is intended by heaven is neither the supreme heaven nor a garden on earth, but instead a heaven located between this world and the hereafter. This heaven bears several qualities of the heaven in the hereafter such as constant bliss, being devoid of suffering and pain caused by hunger, thirst, heat and coldness and at the same time, since it is similar to the gardens in this world, it can be said that it lacks some of the hereafter’s heaven’s traits. For example, man is invulnerable to Shaytan and his temptations in the hereafter’s heaven, because he cannot cross the border of Jannat ul-Khold (the eternal heaven), nevertheless, Shaytan is able to enter mithali and barzakhi heavens and deceive those who are weak.
Of course, this theory both justifies the hadith narrated by imam Sadeq (A.S.) and responds to the reasons mentioned for Prophet Adam's heaven being one of the gardens on earth, because:
A. The word "دنیا" isn’t synonymous to earth, so a heavenly creature that doesn’t live in this world but has actually descended from heaven down to it, is consequently considered to be a creature that belongs to this world rather than heaven. Therefore the word ‘dunya’ might cover heavenly creatures also. Therefore, what has been stated in the hadith (جنة آدم من جنان الدنیا) about the garden being one of this world, means that it wasn’t the heaven of the hereafter, but it could have been a garden of this world or the barzakh.
B. The rising of the moon and sun which bring along the night and day can take place anywhere other than in the hereafter, even in a heaven in barzakh.
C. The exit of Prophet Adam brings us to this conclusion that it surely wasn't the heaven of Qiyamat, but also doesn’t specifically imply that it was located somewhere in this world either, hence it's not considered unreasonable for it to have been in barzakh.
D. There are two Barzakhs; one when descending and the other when ascending. Assuming that Adam's paradise was in barzakh, there is no reason for it to have been in the ascending barzakh which is the barzakh between this world and the hereafter (that takes place after one dies).
E. Living in a heavenly garden in this world isn’t a position to descend from.
F. The qualities mentioned for this paradise such as the absence of pain and anguish caused by inward (thirst and hunger) and outward (heat and coldness) factors do not conform to worldly gardens.
In response to those who believe that Adam's heaven was the heaven of the hereafter one must say:
Firstly: Heaven in the hereafter isn't materialistic, rather, it is mithali and even higher than that, while Adam was created from dirt and worldly material. Thus his material body wouldn't be compatible to the hereafter. The eternal heaven is above and beyond the material world and human beings move and proceed to it through perfection and spiritual evolution.
Secondly: The heaven in the hereafter is eternal, thus one who enters, never leaves.
Thirdly: According to the Quran"لالغو فیها ولا تأثیم" "there they are free from laghv (idle talks and nonsense) and sins", sins and laghv cannot take place in the heaven of the hereafter.
This viewpoint doesn’t contradict what imam Ali has said either; for it is possible that the promise that God gave to Adam regarding him returning to his first position, was actually referring to the ascending barzakh in which takes place before jannat ul-leqah.
 Jubran Mas’ud, Al-Bara’ed Dictionary, vol. 1, the term “جنة”; Muhammad Beheshti, Saba Dictionary, the term “جنة”.
 Mohammad Mo’in, Mo’in Dictionary, vol. 1, the term “بهشت”.
 Tafsir of Fakhr Razi, vol. 3, pg. 3.
 Tafsir Nurul-Thaqalain, vol. 1, pg. 62.
 Tafsir of Fakhr Razi, vol. 3, pg. 3.
 Nahjul-Balaghah, sermon 1.
 Tafsir of Fakhr Razi, vol. 3, pg. 4.
 Abdullah Javadi Amoli, Tafsir Tasnim, vol. 3, pp. 331-332.
 Abdullah Javadi Amoli, Tafsir Tasnim, vol. 3, pp. 356-357, in order to earn how Adam entered the barzakh with his material body, see: ibid, pp. 332-333.
 For further information on this subject, refer to: Al-Mizan, vol. 1, pg. 212; Tafsirul-Quranil-Karim, vol. 3, pp. 80-84; Tafsir Tasnim, vol. 3, pp. 329-357.
 Of course, presenting an explanation for material resurrection is what has driven Islamic thinkers to have different views, for instance, Mulla Sadra believes that the body in that life has to correspond with that life.