I couldn’t find this exact list anywhere else, so I made one for my own reference. Hope it’s helpful for you.

This is a list of when dungeons unlock in The Elder Scrolls Online Dungeon Finder. When you play ESO you can enter dungeons as you find them in the wild, but to queue up and enter a dungeon from anywhere on the map you need to use the Dungeon Finder. In addition, everyone in your group must have a dungeon unlocked in order for your group to queue up for it.

By Level:

10 – Dungeon Finder Unlocked
10 – Fungal Grotto I
10 – Spindleclutch I
10 – The Banished Cells I
12 – Darkshade Caverns I
14 – Elden Hollow I
16 – Wayrest Sewers I
18 – Arx Corinium
20 – City of Ash I
22 – Crypt of Hearts I
24 – Direfrost Keep
26 – Tempest Island
28 – Volenfell
30 – Blackheart Haven
32 – Blessed Crucible
34 – Selene’s Web
36 – Vaults of Madness
37 – Elden Hollow II
38 – Wayrest Sewers II
39 – Fungal Grotto II
40 – Spindleclutch II
41 – The Banished Cells II
42 – Darkshade Caverns II
43 – Crypt of Hearts II
44 – City of Ash II

In addition, the following types of dungeons unlock at these levels but I am not sure if they are accessible in the Dungeon Finder:

45 – DLC Dungeons (Dungeon Finder?)
45 – Undaunted Pledges (Dungeon Finder?)
49 – Veteran Dungeons (Dungeon Finder?)