The ruins are northwest of Gnisis but you can also get there by traveling to Ald Velothi and following the coast to the west. If you happen to have a Dwemer Tube already, you can give that to Edwinna, as any Dwemer tube will do. You can find them in many Dwemer ruins; check the crates, chests, and barrels.
Upon returning to Edwinna with the tube you are rewarded with an additional ten increase in disposition, to go with the five you already received when you accepted the mission.
One in Gnisis Eggmine. The door of the mine is locked (level 45), but no one seems to care if you pick the lock or open it with magic (you could bribe the guard nearby into giving you the key, or he will also give it to you if you are in the Legion. Another way is if you have a miners pick in your inventory.). Make your way into the Lower Eggmine, then east to the buried ruin of Bethamez. Near the table, and on the ground, you'll find a Dwemer Tube.
One in Vorar Helas' house, Balmora. It's in the basket behind him.
If you refuse to give the tube to Edwinna, her disposition drops by 10. The disposition drop also occurs if you refuse to get the tube in the first place.
The following Journal ID and Index codes can be used with the Journalconsole command to manually update the quest to a certain point.
Dwemer Tube from Arkngthunch-Sturdumz (MG_Science)
Index
Finishes Quest
Journal Entry
10
Edwinna asked me to retrieve a Dwemer Tube from Arkngthunch-Sturdumz. Edwinna thinks Arkngthunch-Sturdumz is west of Ald Velothi on the coast. If I follow the coast from Ald Velothi I should be able to see it.