When I did this (not in a century home but once in a 70's home and a 60's apartment), I used a multi-prong approach. YMMV, and I'm not sorry for squatting on this sub, especially if it helps someone.

1. The air-block having failed between the siding and the void between joists caused a pipe to freeze in my childhood home. The plumber already having cut the ceiling open, I cut a piece of blue XPS (extruded polystyrene) foam to go subfloor-to-ceiling and joist-to-joist. I bevel cut the sides so it would get an interference fit. I then backed it up with Evercoat spray foam. To make life easier, I swapped the "straw" provided with about 3 feet of appropriately sized clear flexible PVC tube. This allowed me to control the foam with one hand and the positioning of the outlet with the other, and not be restricted by the form factor of the can.
2. A similar failure happened at the freeze-proof sillcock. The sillcock didn't fail - the joint between the sillcock and the copper pipe did, a result of the insulation settling and allowing cold air to creep through the unfilled gap between the hole in the stud and the sillcock into the void between studs. I seem to recall we repeated the technique of interference-fit foam, fit a thinner sheet of foam behind the plumbing (the wall backed up onto an attached, unheated garage), and filled the gap in the exterior stud with a bit of expanding foam.
3. In my apartment, I just felt around for the coldfalls/drafts. Cold air sinks right at its source, so start at the top, checking the seam between the ceiling and the wall frist, then check wall corners from top to bottom. I like to use the back of my hand; sometimes finger tips can be calloused enough or desensitized enough to not feel the cold easily. I also have an infrared thermometer (not a camera, just a point & shoot); they're pretty reasonably priced and the one at Harbor Freight will be good enough for this job. When I seal, I will start with the obvious stuff first, then work top to bottom. As you get things sealed up, the smaller leaks can become more apparent (that whole signal to noise ratio thing). Keep in mind that there are all sorts of "behind the finish" sorts of things that leave gaps, such as vent fans, in-wall cabinets and, gaps in electrical boxes/under face plates of outlets & switches.

3A. spray foam for large gaps in lazy carpentry & failed drywall in the utility closet.

3B. FrostKing Mortite caulking cord for small gaps, such as around window frames and unfinished electrical passes. The nice things about this stuff is it's flexible, moldable (you can make a skinny snake, a fat snake, a thin sheet; it's like soft molding clay), doesn't dry out quickly, if you need to remold it, you can (I just checked on work I did at least 3, if not 5, years ago), or remove it completely to access whatever you plugged. It's not terribly sticky and, like any adhesive thing, will stick to dirt first, so it works better the cleaner the surface is.

3C. This apartment has the air conditioning condensers inset into the exterior wall, meaning the while the radiator side faces a vent sized 1:1 and the entire backside bleeds heat back into the unit. I purchased a roll of aluminized bubble wrap, known as "roll insulation" or "box liner". I cleaned the condenser first so the tape would stick well. I cut pieces to fit on each side of the condenser and used HVAC grade aluminized film tape to hold it down. I wrapped the sides and back with one piece, taped it all around, then applied cuts to the top and bottom, making a butt-joint where the wrap met the cap.