Replacing heel tips is really not hard if you still have enough metal to grab with a pair of pliers. (Vise-grips or the like come in handy here.) From your post it sounds like the heel tip is pretty much gone and the metal nub is all that is left. That nub should have a rather well-defined head on it -- grab that head tightly with a pair of vise-grips and then pull the pin out of the heel. (High heels are usually reinforced with a steel tube running up the center of the heel. This tube provides a nice place to insert the heel tip pin.) Once you have the pin out, you will have a nice clean hole for the new tip. Insert the new pin into this hole and align the tip with the shape of the heel. Push the pin in until the heel tip stays put all by itself. Then hold the shoe by the toe box with the heel facing downward and whack the heel tip on the edge of a nice, robust surface (like a workbench) as if the shoe was a hammer -- think "Nikita Khrushchev" here

. This will drive the tip pin up into the heel tube and seat the tip right where it belongs.
There are a couple of other threads about this here in the "repair and modifications" area, even about times when things went wrong. Stiletto heels, especially, are subject to a lot of wear and this repair is very common.