The correct options are
A After my shift
C fine dining
An adjunct is a word, phrase or clause that can be eliminated from the
sentence, without affecting it grammatically. The sentence would still
make sense without an adjunct. Adjuncts are usually adverbs, adverb
phrases or adverb clauses. When the adverbial phrase "After my shift" is removed, the sentence is grammatically correct. Similarly, when the compound noun "fine dining" is removed, the sentence is still complete with the subject and verb intact. 'Fine dining' is a noun adjunct as it modifies the noun 'restaurant'. (Usually adjunct is an adverb/adverbial as it modifies a verb or an entire clause.) Hence both of these are adjuncts and options A and D are correct. "Went" is a verb and "to a fine dining restaurant" is a prepositional phrase. While omitting each of these the sentence sounds incomplete, hence options B and C are incorrect.