When we talk about "seeing fit" to do something, we are usually referring to making the decision to do it based on our own judgment or preference. There are many synonyms for this phrase, including "decide," "choose," "determine," and "opt for."
Other synonyms might include "elect," "select," "settle on," "make up one's mind," "resolve," or "conclude." Essentially, any phrase that conveys a sense of making a conscious decision based on one's own preferences or judgment could be considered a synonym for "see fit." Ultimately, the choice of which synonym to use will depend on the context of the sentence and the tone of the writing or conversation.