"I eat breakfast in the cafeteria."
に、へ are often used when something happens -at- a time, and more often pointing out destination and direction, de is used when something happens -at- a place.
They have other uses, but i'm limiting them to what has been discussed in previous duolingo tests. Have a read here. http://www.punipunijapan.com/japanese-particle-ni-e/
I should reply to this with slight corrections, there are other uses and meanings: 日曜日で。。。indicates something happens on sunday(s) in general
日曜日に。。。indicates that something happens on sundays as opposed to other days
夜で寒いです (yoru de samui desu) is best interpreted as "It is (in general) cold at night"
夜に寒いです is best interpreted as "It is (as opposed to daytime, for instance) cold at night"
The only difference (apart from kanji instead of hiragana) that I spot between your sentence and Duolingo’s is the honorific prefix お before あさごはん ; now, I may be wrong, but I think that it is not possible to use it for this word. A quick search on the Internet (both the Wiktionary — whether English- or Japanese-speaking — and using a search engine) does not seem to really bring up this word, so I will stand by my hypothesis.
PS: this just in: in another Duolingo sentence, I stumble upon おひるごはん, so maybe yours was right after all… If you have the chance, try reporting your answer as valid.
私は is relatively pointless inclusion as it is already implied by polite ます, and furthermore statements about activities that do not specifically state an object (another person, for instance) are about self.
It is not explicitly wrong, but it is needless. 私は「Me (topic)」食堂で「Dining room at」朝ごはんを「breakfast which」食べます 「eat/will eat, polite」