How can I repair an air conditioner drain line that is broken flush with the wall?
However you end up fixing this do plan to use a more repairable solution that used by the original installer. It is an insane approach to cement or stucco in a glued plastic fitting like this. As a minimum the part that gets cemented in place should be made out of metal with brass or bronze being preferred over an iron type fitting. The outside pipe should be fitted to the cemented in part via a threaded connection.

If you must repair this with minimal disturbance to the cement or stucco, (its hard to tell which from the picture) then I would see a number of possibilities...

a) Work at drilling and carving out the glued in inner pipe piece bit by bit till you get it the point where you can fit a new piece of pipe in its place. You have to use much care for this because the process could put excess torque on the remaining pipe in the wall and lead to possible further breakage. 

b) Try to find a suitably sized pipe thread tap and cut threads into the inner diameter of the pipe stub. Once this is done you can fit it up with the proper type of barbed brass pipe nipple fitting. To this you can attach a flexible piece of hose to go out the 2 to 3 feet from the foundation.

If you have access to the area inside the wall you may be able to simply pull the existing fitting out of the cement and install a newer more suitable type of exterior transition that the method used. 

If the wall is stucco you could take a chisel to the area around the broken off fitting and enlarge the hole enough to get access to the pipe. Then you can fit up the proper type of pipe fittings and re-patch the stucco around a metal transition fitting. Stucco patching is a fairly straight forward task and should be able to completed successfully by a diligent DIY home owner.