Although it is technically correct, だって has a particular nuance which is hard to describe; I would avoid using it with most of my teachers. Little kids use it a lot and adults tend to stay away from it, except maybe with friends or family or co-workers (but probably not usually someone in a higher position). It is on the informal side. A situation where だって would be appropriate in Japanese is when a kid wants some candy at the store, the mom says no, and then the kid tries to appeal to her. "But Mom! I'm starving. Please, please, please!" If the kid says だって、はらへったもん, it means that she should understand why he needs the candy because he is starving. "I already told you" also is a phrase that can be nuanced with　だって in Japanese: だって、いてったよ。 Anything with だって in it, regardless of the formality of the situation, has the nuance that the speaker expects that the listener should understand what he/she is trying to convey. In your case, the nuance is that the teacher should know that particular restaurant is good, and that further debate about it is kind of pointless, or something like that. Hope that helps.

In this case, だって was used as because. Usually だって means as same as なぜなら/because. So you can add an explanation of the reason why you like it, after だって/なぜなら. In this particular case, 私 is saying "(このお店は)もっとおいしい" as an explanation of why you recommend this restaurant. だって、このお店はもっとおいしいんです。 →なぜなら、このお店はもっとおいしいんです。 Those sentences mean basically the same; but we tend to use だって more often than なぜなら in daily conversation.

If I'm talking to my teacher, I would say 私：私はこのお店のほうがいいと思います。このお店はもっとおいしいからです。 So I'm basically with Jay about usage of だって. At least I'd not use it when speaking to someone whom I should be polite to.