Is there a list of the 'levels allowed' range for joining public games of a particular quest and difficulty?

Solution 1:

Normal difficulty

Act 1

1. The Fallen Star: 1-6
2. The Legacy of Cain: 1-9
3. A Shattered Crown: 2-10
4. Reign of the Black King: 4-13
5. Sword of the Stranger: 5-13
6. The Broken Blade: 6-14
7. The Doom in Wortham: 8-16
8. Trailing the Coven: 8-16
9. The Imprisoned Angel: 12-20
10. Return to New Tristram: 12-20

Act 2

1. Shadows in the Desert: 12-20
2. The Road to Alcarnus: 13-21
3. City of Blood: 14-22
4. A Royal Audience: 15-23
5. Unexpected Allies: 15-24
6. Betrayer of the Horadrim: 17-25
7. Blood and Sand: 18-26
8. The Black Soulstone: 18-26

Act 3

1. The Siege of Bastion's Keep: 21-29
2. Turning the Tide: 22-30
3. The Breached Keep: 23-31
4. Tremors in the Stone: 23-31
5. Machines of War: 23-31
6. Siegebreaker: 24-32
7. Heart of Sin: 24-32

Act 4

1. Fall of the High Heavens: 25-33
2. The Light of Hope: 26-34
3. Beneath the Spire: 27-35
4. Prime Evil: 28-36

Nightmare difficulty

Act 1

1. The Fallen Star: 29-35
2. The Legacy of Cain: 31-36
3. A Shattered Crown: 31-37
4. Reign of the Black King: 33-38
5. Sword of the Stranger: 33-39
6. The Broken Blade: 34-39
7. The Doom in Wortham: 35-41
8. Trailing the Coven: 35-41
9. The Imprisoned Angel: 38-43
10. Return to New Tristram: 38-43

Act 2

1. Shadows in the Desert: 38-43
2. The Road to Alcarnus: 39-44
3. City of Blood: 39-45
4. A Royal Audience: 40-45
5. Unexpected Allies: 41-46
6. Betrayer of the Horadrim: 41-47
7. Blood and Sand: 42-47
8. The Black Soulstone: 42-47

Act 3

1. The Siege of Bastion's Keep: 44-49
2. Turning the Tide: 45-50
3. The Breached Keep: 45-51
4. Tremors in the Stone: 45-51
5. Machines of War: 45-51
6. Siegebreaker: 46-51
7. Heart of Sin: 46-51

Act 4

1. Fall of the High Heavens: 47-52
2. The Light of Hope: 47-53
3. Beneath the Spire: 48-53
4. Prime Evil: 49-54

Hell difficulty

Act 1

1. The Fallen Star: 49-52
2. The Legacy of Cain: 50-53
3. A Shattered Crown: 51-53
4. Reign of the Black King: 51-54
5. Sword of the Stranger: 52-54
6. The Broken Blade: 52-55
7. The Doom in Wortham: 53-55
8. Trailing the Coven: 53-55
9. The Imprisoned Angel: 54-57
10. Return to New Tristram: 54-57

Act 2

1. Shadows in the Desert: 54-57
2. The Road to Alcarnus: 54-57
3. City of Blood: 55-57
4. A Royal Audience: 55-58
5. Unexpected Allies: 55-58
6. Betrayer of the Horadrim: 56-58
7. Blood and Sand: 56-59
8. The Black Soulstone: 56-59

Act 3

1. The Siege of Bastion's Keep: 57-60
2. Turning the Tide: 57-60
3. The Breached Keep: 58-60
4. Tremors in the Stone: 58-60
5. Machines of War: 58-60
6. Siegebreaker: 58-60
7. Heart of Sin: 58-60

Act 4

1. Fall of the High Heavens: 58-60
2. The Light of Hope: 59-60
3. Beneath the Spire: 59-60
4. Prime Evil: 59-60

Inferno difficulty

Inferno difficulty isn't available until you reach level 60.

Solution 2:

The Diablo 3 Database has the "levels allowed" range for each difficulty and quest on the respective quest page. For example, the first quest in the game, The Fallen Star has the following ranges listed on the right side of the page.

Normal Levels: 1-6
Nightmare Levels: 29-34
Hell Levels: 49-52
Inferno Level: 60