There are several synonyms that can be used for the phrase "walked unsteadily". This could include terms such as stumbled, faltered, or wobbled. Some other possible options might include staggered, weaved, or swayed. Each of these terms implies a level of instability or lack of balance, which can be useful in conveying a particular mood or tone in a piece of writing. Depending on the context, some of these synonyms may be more appropriate than others, so it's important to consider the specific connotations and nuances associated with each word when choosing which one to use.