There are ten Dunmer strongholds, arranged in a rough ring around Red Mountain. These strongholds are a remnant of the time when the Dunmer were defending themselves from the Nords and the Propylons were the means of moving troops, supplies and equipment between the strongholds. For reasons that I detail below, I did not think these teleporters were worth including in the travel section, but someone suggested that I do so. The more I thought about it, the better the idea seemed, so here it is.
The existence of the strongholds isn't any great news. You are sent into Kogoruhn as part of the Main Quest and various faction quests will send you into the Andasreth, Berandas, Falasmaryon, Indoranyon, Rotheran, and Telasero strongholds. You'll pass within spitting distance of the Marandus stronghold on one of the first quests from Ranis in the Balmora Mages Guild and one of the Morag Tong Writ quests will take you to the roof of the Hlormaren stronghold. That leaves the Falensarano stronghold (near the easternmost point of the Grazelands, more or less southeast from Tel Vos and south-southeast from Tel Mora) and Valenvaryon stronghold (east of the Urshilaku Ashlander camp, near the coastline) that you'll either need to learn about from someone like me or stumble across on your own.
Each Propylon Chamber has two teleporters which will take you to one of the other strongholds, but you must have the appropriate index to activate that particular Propylon. Obtaining the indices is an undocumented quasi-quest. Since each index weighs two pounds, you'd need to tote an extra 20 pounds of equipment to be able to make full use of these teleporters. Additionally, the teleporters work by going around the ring (I recall someone calling it "running the bases"). You can't cut from one side of the island to the other. Instead, you must hop from stronghold to stronghold until you get into the general vicinity of wherever it is that you want to go. And none of the strongholds are reasonably close to points where you would be able to grab some other form of fast travel. Consequently, I rate these chambers as a dubious convenience at best in the release-version of the game. But it's the only free fast-travel in the game.
Shortly after the game's release, however, Bethesda did a plugin (called, appropriately enough, the "Master Index Plugin") that lets you consolidate the ten into a single "Master Index" that also links into the Caldera Mages Guild. The quest involves retrieving all ten indices and returning them to the quest-giver in the Caldera Mages Guild. Once that is accomplished, you get the Master Index that lets you go to any stronghold from Caldera or to Caldera from any stronghold, as well as being able to "run the bases" as if you had all of the indices. This addition may make the Propylon Chambers a more attractive form of travel.
If you'd rather forgo the plugin (which has decent enough directions on where to find each index), here's where you can retrieve the indices:
Andasreth: on a bookshelf on the top level of the Hlormaren stronghold. You can get to it from the roof entrance or fight your way up from the ground entrance.
Berandas: on a bookshelf under the main dome in Barandas Demnevanni's home (Arvs-Drelen) in Gnisis (the Berandas stronghold itself is crawling with Daedric critters and you can pick up a Daedric Dagger, Daedric Spear, Daedric Arrows [a couple of 'em] pretty much freebies, and whatever Ebony/Daedric stuff you might find on the Dremora)
Falasmaryon: in front of the stone in the shrine at Maar Gan
Falensarano: at the top of the Forgotten Galleries in the Maelkashishi shrine (more or less southeast of Khuul). Someone in the game actually knows about this index. You can find out about it by talking to Crazy-Legs Arantamo in the Canalworks section of Vivec's Foreign Quarter (use the "little secret" dialog option).
Hlormaren: on a window sill at Irgola's Pawnbroker shop in Caldera
Indoranyon: on a table near Divayth Fyr at Tel Fyr
Marandus: in a storage room on the lower level of the temple in the St. Olms canton in Vivec
Rotheran: Rols Ienith has it. He's in the Communal Hut at the Rotheran stronghold (how convenient)
Telasero: in one of the treasure troughs on the lowest level of the Sixth House base in the Telasero stronghold (another "how convenient"?)
Valenvaryon: on a table in the Wise Woman's hut in the Urshilaku Ashlander camp