Walking
Walking is possibly the best way to see the sites of Nerja, and of course it is free! Walking allows you to take whichever route you want with as many stops as you please, allowing you to view only the things you really want to see and spend as long as you wish doing so. Especially the Old Town, as streets are narrow and sloping so you cannot pass with cars, and maneuvering a bicycle can be difficult. Walking also means allows you to stop off at as many bars and cafés as you like along the way!
Horse and Carriage
Another popular and traditional way to travel around Nerja is by horse and carriage. This is a unique and relaxing way to travel around the town.You can find horse and cariages in the Plaza de Los Cangregos; they can take you on a tour of the town. A trip costs 30 Euros (but prices can vary). They are a lovely eco-friendly way to travel (the horses are well cared for) and are a romantic way to spend an evening if you are having a romantic gettaway. As a bonus that they can take you where cars cannot.
Taxi
There are many taxi ranks scattered throughout Nerja, and if you are not near to one of these, you can hail a passing taxi from the road, they are happy to stop and pick you up. However in the old town cabs pass less frequently so you can call one on 952 520 537. Traveling back to the villa after visiting the town can save time and energy and is very reasonably priced. (7€ 2015/2015).
If you are taking a taxi to the airport then it is better to book in advance, or arrange to travel with an airport transfer company, to get the best prices.