Rate adaptation is a key mechanism in current IEEE 802.11 networks and next-generation cellular systems. Observing that the operating time scale of rate adaptation is usually much smaller than the user association and scheduling, we study a joint design of wireless user association and scheduling and rate adaptation with different time scales to maximize cumulative system throughput while guaranteeing desired fairness among users. We develop a maximum-weight type user association and scheduling algorithm that combines the virtual queues (tracking the scheduling debt for each user to ensure the desired fairness guarantee) and Upper Confidence Bound (UCB) estimates in its weight measure; each selected user then adopts the UCB algorithm to perform rate adaptation in a smaller time scale. We show that our proposed algorithm yields a cumulative regret growing with the square root of the time horizon up to a logarithmic factor, and achieves zero cumulative fairness violation after a certain number of time frames. We demonstrate the efficiency of the proposed algorithm via simulations using synthetic and realistic data traces.