Yes, there is a sun and moon. The Sun is a "She" according to hobbits and elves. I think they were based off the Two Trees of Valinor.
The sun is the last fruit of Laurelin and is guided by the fire spirit Arien. She was one of the few fire spirits not corrupted by Melkor; the corrupted ones became Balrogs.
The moon is the last flower of Telperion and is guided by the hunter Tilion. He is a bit wayward in his travels, being enamored of Arien and trying to come close to her.