Did a similar trip solo last month and it was fantastic. Fell in love with Seville - wonderful city. I flew Ryanair to Malaga (cheapest option) got the train (only 10 minutes) from airport to Malaga centre and stayed in a cheap hotel, next day got the train to Seville (2 and half hours journey, cost 24 euros for the slightly slower train - fast one was nearly double that price and only 45 minutes quicker). 4 nights there. Then on to Cordoba by train (2 nights, 45 minute journey) then Granada by bus (train station is closed so even if you book the train there is a bus replacement for half the journey so I booked the premium Alsa bus instead (free wi-fi, single seats etc). 3 nights there. Then on to Ronda (3 nights) and then train back to Malaga for a bus to Nerja (4 nights). Then bus back to Malaga for flight home.
In order of preference I liked Seville, Granada, Ronda, Cordoba and Nerja (all were pleasant places, I just liked the bigger cities more).
One night and day was probably enough for Cordoba (or do it as a day trip from Seville). Alhambra in Granada was amazing - book tickets in advance though! If I did it again I would probably have skipped Nerja and spent more time in Granada and Seville. Felt very safe everywhere, especially Seville. Granada was a bit more 'gritty' in some parts (more grafitti, sometimes people stared at you a bit but probably just curiosity...as I was obviously not Spanish). I did just wander all over the place though, as I like doing that in a foreign city.
Top tips:
Download the Alsa (bus) and Renfe (train) apps - makes booking much easier and you can use mobile tickets. Trains and buses are good and easy to use - on the trains they even make the announcements in both English and Spanish.
Learn a few Spanish phrases - not everyone speaks English so it helps, even just for ordering food, coffee, wine/beer etc. As well as the basics like hello (Hola!), goodbye (adios/hasta luego, thank you (gracias) , you're welcome (de nada) etc. Youtube videos are good for learning or just use Google translate app when you are there. :)
Try the more 'local' tapas places - crowded, but good cheap food and drink and friendly vibe. It helps if you like seafood. :) In Granada you get a free tapas with every drink you order!
In Seville, see the Alcazar and the Cathedral (climb the bell tower- great views), Plaza de Espana, Triana market (Mercado de Triana), wander around the Old Town and Macarena (impossible not to get lost - use Google maps!), go up Las Setas (mushroom shaped thing - 3 euros) for sunset.
Airbnb is good -- I got a nice 2 bedroom apartment in Seville all to myself for same price as a cheap hotel (£27 a night), stayed in a converted recording studio in Ronda with a shared outdoor terrace and a 3 bedroom flat in Granada with a sunny balcony and lounge which had views of the city - all for under £30 a night (it was off season though).
I would not bother with a tour, but then to me the advantage of solo travel is go where you like for as little/long as you like and a tour takes that away, feel a bit rushed and also a bit like a sheep being herded around. :) (That's my experience anyway - plus side of course is you meet people and have companions for meals, which is nice).
Any questions - ask away and I will help if if I can. Definately recommend it though - maybe avoid mid-summer though as it gets seriously hot apparently!
Some good info here: www.theguardian.com/travel/2017/apr/08/seville-city-guide-what-to-do-best-hotels-restaurants-bars