The English sentence being "I brush my teeth, wash my face, and have breakfast every day."
My translation was 私は毎日歯で磨いて顔で洗って朝ご飯を食べます.
The given answer was 私は毎日歯を磨いて顔を洗って朝ご飯を食べます.
Given the context, I thought で could be used because I'm marking the location/tool/method/condition for an action.
But that's not correct, right? Because 歯 and 顔 should be treated as direct objects and not any of the above?
If you were marking location, consider what you'd really be saying in English.
I brush on my teeth, wash on my face, and have breakfast every day.
When you're using で you'd indicating where the action is occurring. Consider how odd this sounds in English. It's the same in Japanese: unless there's something on your teeth that you were brushing or something on your face that you were washing.
If you're using で to mark the location of an action, you're marking the location within which the action was occurring.
図書館で本をよみました。
I read my book at the library.
You could say
台所で歯を磨いて。。。
I brushed my teeth in the kitchen and ....
If you're thinking of your teeth or your face as a tool, then the rendering in English would be to the following affect:
I brushed with my teeth, and I washed with my face....
Hopefully, you're not using your teeth as a tool for brushing something (you'll wear your teeth away and there are probably better tools available). When you're brushing your teeth, you're using a toothbrush, not your teeth.
歯ブラシで歯をみがきました。
I brushed my teeth with a toothbrush.
And unless you're into strange sexual practices, you're probably not washing anything with your face.
ハンドタオルで顔を洗った
I washed my face with a washcloth.
You should understand the “location” marked by で as a “setting” or “surroundings” within which the action of the verb takes place, rather than a pin-point location to which the effect of the action is applied. I don’t know how to explain this with words so it is understood by learners, but I see what is marked by the location-で as bigger than the action. Surroundings are always bigger than what they surround, right?
If what is marked by で is smaller than the action, it tends to be understood as indicating means, method, or tool. (で has other functions, of course, but let's ignore them for now not to complicate the things.)
Try to compare the sizes of the things involved in the following sentences to see if this advice makes sense to you.
新幹線で大阪に行った。
新幹線で弁当を食べた。
割り箸で弁当を食べた。
大阪でUSJに行った。
In any case, neither usage matches your scenario. It must be hard to imagine a situation where your teeth or face is a setting for some action, and you don’t use those things to brush or wash something, either. Meanwhile, the verbs 磨く and 洗う both require a direct object (like the corresponding English verbs) unless it is specifically omitted as obvious from the context. So を is the right choice.
Forgive me if I'm wrong, I'm also a beginner, but by "で could be used because I'm marking the location/tool/method/condition", teeth meets none of theses conditions. location as in in the bathroom, tool as in the toothbrush, method as in a specific method for brushing(?), condition as like on saturdays, etc. Same for face. Your original translation has a meaning closer to you brushing something with/by using your teeth. In this case を is indeed the correct answer as the teeth is the direct "object" being brushed.
My best quick-rule for sensible use of the で grammar marker.
The で is used most often like the English word "within".
Example:
図書館で本をよみました。
Translates to:
Within the library, I read my book.
More natural English is probably:
I read my book at the library.
But this rule has served me well in most cases.
