"Sidle up" is a phrase commonly used to describe the act of approaching someone in a friendly or casual manner. If you are looking for alternative words that convey a similar meaning, there are several synonyms you can use. For instance, words like "approach," "converge," "draw near," and "move towards" can be used to describe the act of getting closer to someone. Other great synonyms for "sidle up" include "mingle," "rub elbows," "fraternize," "socialize," and "network." Regardless of which synonym you choose, the most important thing is to approach others respectfully and with genuine interest, building human connections along the way.