"I looked around."
Translation:Mi sono guardata intorno.
I think it is similar to what my Ancient Greek (?) teacher called "dative of interest". The reflexive is there not as the object of "intorno" ('around myself") but a literal translation might be I looked around [because I was curious, to find out where I was, etc.]. Cf. the French "Je m'en vais" - does NOT mena I go away from myself, but simply I go away [from where I am, i.e. from here]. You will start to really learn a language from the inside when you realize that a literal word-for-word translation is not always appropriate. It may work sometimes (more often, the closer the languages are historically), but what you really want is not the word-for-word, but the equivalent meaning, nuance, tone, level of discourse, etc. in the 2nd language. That is why machine translations are sometimes unintelligible, esp when the languages have different syntax. To convince yourself, try translating a few lines of poetry from Japanese or ancient Greek or Russian into your native language with Google translate. There is a good chance the output, while word-for-word the equivalent, will not be grammatical and may not even be understandable.
Since you included "mi" in your sentence, you apparently wanted to use the reflexive form. If so, the auxiliary verb "essere" is required. The correct sentence then is: "Mi sono guardato intorno."
If you did not intend to use the reflexive form, then the use of "mi" is incorrect. In that case, "ho guardato intorno" is the correct sentence.
"Essere" is used as the auxiliary verb for reflexive verbs. 'Mi sono guardato intorno" is the reflexive format. Apparently one can use a non-reflexive format in this instance. In that case the sentence would be: "Ho guardato intorno." See the first comment in this forum for additional information.