When we use accuracy, we assign equal cost to false positives and false negatives. When that data set is imbalanced - say it has 99% of instances in one class and only 1 % in the other - there is a great way to lower the cost. Predict that every instance belongs to the majority class, get accuracy of 99% and go home early.
The problem starts when the actual costs that we assign to every error are not equal. If we deal with a rare but fatal disease, the cost of failing to diagnose the disease of a sick person is much higher than the cost of sending a healthy person to more tests.
In general, there is no general best measure. The best measure is derived from your needs. In a sense, it is not a machine learning question, but a business question. It is common that two people will use the same data set but will choose different metrics due to different goals.
Accuracy is a great metric. Actually, most metrics are great and I like to evaluate many metrics. However, at some point you will need to decide between using model A or B. There you should use a single metric that best fits your need.
For extra credit, choose this metric before the analysis, so you won't be distracted when making the decision.