Ranmir lives with his sister Birna in Birna’s Oddments, a shop in Winterhold. Like the shop’s name suggests, it sells general items such as soul gems, potions, and odds and ends. You will likely find him in Winterhold’s inn, The Frozen Hearth. It is possible that he dies during the Containment quest from the College of Winterhold, though it is possible to save him.
One way to prevent Ranmir’s death is as follow: After completing the quest Revealing the Unseen (and starting Containment) and surviving the blast from Ancano’s fiddling with the Eye of Magnus, you will run outside to find that Savos Aren has been killed in the blast. Tolfdir will tell you to go check on Winterhold to make sure it is safe. Right after he instructs you to do this, open your map and fast travel to Winterhold. Kill all of the enemies in town. When you go to Birna’s Oddments, probably located upstairs, you should find Ranmir, unharmed and fully alive.
When looking through his corpse, you will find The Key to Ranmir’s House, which unlocks an adept level lock into the shop. Although, using the key still counts as trespassing, and Birna will call the guards if she notices you.
Although not classified as a quest, many of the inhabitants of Winterhold remark upon Ranmir’s drinking problem due to a soured relationship. If you talk to the innkeeper of Winterhold and his wife they will eventually mention Isabelle Rolaine, Ranmir’s former girlfriend and lover, who skipped out on him. The thief Vex knows of her current whereabouts and directs you to Isabella (found in Hob’s Fall cave).