Thanks for all of the replies.
I know for sure the radiator is leaking where Rick Norwood mentioned. Found it yesterday. Picking one up to deal with over the holiday. Surprisingly not as expensive as I thought. Any advice on that? Anything I should be aware of that might not be typical for this kind of job?
If the heater core is indeed bad, I'll wait until this fall/winter to deal with. I ran heat this morning and didn't smell a thing, but ran it last night and the smell wouldn't go away. It certainly doesn't seem like the typical symptoms that I've read about.
Thanks again.