If the added thought, word, or expression is not essential to the main idea of the sentence, use commas. Read the sentence without the added material. If the information is not crucial to the reader's understanding, then set it off with commas. Put a comma around an interjection or afterthought that interrupts the flow of the sentence. Again, use commas if you can read the sentence without the added material and if the information is not crucial to the reader's understanding.
Independent clauses can stand alone as sentences.
They have an active subject and an active verb. If you do not add a comma between two independent clauses, you have created a run-on. Columbia has a lot of great restaurants, and its nightlife is fantastic. Put a comma around words that would otherwise mislead the reader. It will take the reader a little back-tracking to figure out that a comma should be after the word eating.