Where is Cicero after he is spared?

If you spare Cicero in the quest A Cure For Madness then he will be available later in the quest line from the Dawnstar Sanctuary. Specifically, he will appear when Hail Sithis has been completed and the Dragonborn first leaves the Sanctuary through the front door.

After some amusing dialogue, he will enter the sanctuary (assuming you don't take him on as a follower straight away) and can be found next to the Night Mother's coffin on the balcony near the stairs. It's fairly gloomy in there even with the furnishings purchased so a detect life spell may help until you get used to where he will be.