There are several synonyms for the phrase "wobbles about" such as wavers, staggers, sways, totters, reels, shakes, quivers, shimmies, and oscillates. These synonyms can be used to describe a variety of movements, from a person stumbling around to an object vibrating. Each word has its own nuance, and understanding their differences can help to add more descriptive detail to your writing. For example, "sways" may suggest a gentler swaying motion, while "staggers" may imply a more unsteady movement. Overall, using synonyms can help to keep your writing varied and interesting while still conveying the desired meaning.