Do paradise and hell exist within the universe? It's so vast that humans haven't even been the other galaxies.
Paradise cannot be inside current universe of us living in it. Because size of only one garden of one believer in paradise is larger than earth and all the skies (considering our universe is only the first sky).
And hasten to forgiveness from your Lord and a garden as wide as the heavens and earth, prepared for the righteous http://tanzil.net/#3:133
But Quran also says:
They urge you to hasten the punishment. And indeed, Hell is encompassing of the disbelievers http://tanzil.net/#29:54
According to Arabic grammar this verse means that Hell already is encompassing disbelievers. But God has made a barrier between them and fire so that they do not feel it. By death this barrier is removed and they see and feel it. This also the same about paradise.
So where is it? it is in a parallel universe around us that all cannot see it. But only few real pious people can see it. If we try and become a real pious believer we can see Paradise and Hell already before death.
Quran says if one reach to the rank of "knowledge of certainty" by being pious, can see the Hell.
No! If you only knew with knowledge of certainty... You surely see the Hellfire. http://tanzil.net/#102:6
According to this verse those who can obtain the "knowledge of certainty" can see the Hell already (before death). And this knowledge is granted by God only to those who are real pious. God himself is teacher of who is pious and teaches him any kind of knowledge:
And be pious about Allah, and Allah teaches you. http://tanzil.net/#2:282
There are hadith saying some Sahaba could see the Hell and also currently such people can be found. But they are rare and also try to not be known because being unknown is what God wants:
That home of the Hereafter We assign to those who do not desire exaltedness upon the earth or corruption. And the [best] outcome is for the righteous. http://tanzil.net/#28:83
A Jew came to question Prophet Muhammad (PBUH) and he told the Prophet that he would accept Islam if the Prophet of Islam gave the correct answers. He asked the following questions:
Does the "Jannat" meaning Paradise exist? If it exists, what is the distance from the earth?
Does the "Jahanam" meaning Hell exist? If it exists, what is the distance from the earth?
Prophet Muhammad (PBUH) replied that Both "Jannat" and "Jahanam" meaning Paradise and Hell exist. The Paradise is up from the earth and 30,000 light years (Noori years) from the earth. The Hell is down and 7 earths distance from the Earth.
The Jew replied that you are right. It is exactly mentioned in our Holy Scriptures and no one knows except few learned scholars among us. So he accepted Islam.