Do we know what Aristotle thought of Alexander the Great?

Short answer: We don't know for sure, as Aristotle never wrote even one word about Alexander the Great himself, or at least none that survives.

Long answer: Although the relationship between the philosopher and the warrior prince has been idealized to a great extent in the Western tradition (e.g. the Secret of Secrets, an 9th or 10th century fake correspondence between Aristotle to Alexander, where Alexander for example credits Aristotle for his conquests, had a cult following in medieval Europe), most modern scholars think that their relationship couldn't have been a very close one. Aristotle spend only about two years as Alexander's teachers in Mieza, and Alexander was a teenager of thirteen years when Aristotle started his education. We have very little concrete knowledge of what went on during those lessons, and of what shape their relationship took after Aristotle left Macedonia. Our only sources come from much later ancient authors of the biographical tradition - and all rather unreliable sources because of the genre's affinity to rumors and sensationalism. But, if somebody is interested, Ingemar Düring (1957), Aristotle in the Ancient Biographical Tradition: 284-8 has a list of comments about the relationship between Aristotle and Alexander by ancient authors.

The sources vary, but the tradition seems to hold that they stayed in contact more or less until Aristotle's death, and that Alexander might have given substantial financial assistance to Aristotle's hometown Stageira and to Aristotle's scholarly projects, namely his school and library. Some authors, such as Plutarch (Life of Alexander 7), seem to believe that their relationship grew cold towards the end of Aristotle's life because of some unspecified mutual mistrust.

Whatever the relationship between Alexander and Aristotle was, it was unlikely one based upon their shared views about politics and the meaning of life. Obviously, lot of the things that Alexander did and stood for are violently incompatible with Aristotle's thought. Just one clear example is Alexander's expansionist hunger for an empire, when Aristotle later in Politics clearly states that, ideally, human societies should be organized around small, self-succient, self-governing poleis, no bigger than what is possible to see in one view (Politics VII.5 1327a3). Aristotle believed in a happy, contemplative life, and that war cannot never be the final end of human life (Nicomachean Ethics X.7). He also seems to be one of these rare philosophers who actually practiced what they preached, so it is unlikely he was proud of Alexander's exploits. Aristotle's remark in NE X.8 1179a10, "it is possible to perform noble acts without being ruler of land and sea", looks like a direct dig at Alexander.