The correct option is
D sleep
In order to fill in the blank with the most suitable form of the infinitive, we need to understand the meaning and usage of 'had better'. 'Had better' is used when a situation, person or a thing is better than the other (to do/to have). If 'had better' is used in a passive (voice) sentence, we use the word 'to' along with the verb. In an active sentence, we do not use 'to' with the verb. The verbs without the marker 'to', are called bare infinitives.As the given sentence is in the active voice, we will use the bare infinitive here.
Option A - 'Slept' is the past form of the verb 'sleep'. As we need the bare infinitive (original form of the verb), we can't use 'sleep' here. Hence, option A is incorrect.
Option B -'Had slept' is used to represent an action or a sentence in past perfect tense. As we need the verb in its original form, we can't use 'had slept' here. Hence, option B is incorrect.
Option C - 'To sleep' can't be used here as the verb in its original form with the marker 'to'. As the sentence is in the active voice, we can't use the infinitive with 'to' here. Hence, option C is incorrect.
Option D - 'Sleep' is a verb in its original form and is a bare infinitive. Hence, option D is the correct answer.
'I had better sleep now unless I want dark circles.'