"Most close at hand" implies something that is easily accessible and within reach. Therefore, antonyms for this phrase would be words that indicate something that is far away or difficult to reach. Words such as distant, out of reach, inaccessible, remote, and far-flung can be considered antonyms as they indicate something that is not easily available or nearby. Furthermore, phrases like unreachable, hard to get, and out of range can also be used as antonyms to indicate something that is not easily accessible. Overall, there are many antonyms for the phrase "most close at hand" that can convey the opposite meaning of easy accessibility.