Limyra is an ancient Lycian town of medium interest, and clearly not worth any extra effort to reach. While its city wall rise higher and more impressive than many other place you can visit, the rest is of limited interest to most. Limyra was named capital of Lycia in the 4th century BCE, but from that point on it seems simply to fade out of history, loosing its rank among Lycian towns at an unidentified point in history.
Theatres of Greco-Roman style often look nice. The one of Limyra dates to the 2nd century CE, but it is neither unique nor terribly large. When all of that is said, there are still large areas to walk through here, Limyra was a sizeable town. Structures along and across the river are nice, especially when the river runs at its full.
There are no facilities of any kind at or near Limyra. Accommodation, food and even transport is arranged for at Finike, 10 km south. Driving here, you may have to ask for directions. There is a road some 7 km from Finike turning east, follow this for 3 km and you will arrive directly at Limyra.