When it comes to synonyms for the phrase "run at," there are a variety of options to choose from. If you're trying to describe an attack or aggressive behavior, you might opt for terms like charge, rush, or assail. On the other hand, if you're talking about a more playful or friendly interaction, you might use words like approach, greet, or meet. Depending on the context, you could also consider terms like advance, advance upon, confront, or tackle. Ultimately, the best synonym for "run at" will depend on the situation, the tone you're trying to convey, and the specific words you want to use to describe the action.