Getting around Granada and Andalucia: car rental vs. taxis and public transit

Sounds like a neat experience!
Hopefully someone will come along who knows that road, but it looks fairly straightforward.
I would lean toward a day rental within Granada because if you are flying into Malaga and driving immediately after an overnight flight, you be right to have some qualms about safety.
If you get the car, I would try to add Antequera.

We had the same predicament while staying in Palermo and wanting to visit the Valley of the Temples in Agrigento. We wanted to see the VT in the evening as the sun set and the temples were lit. That would require a 2.5 hour drive at night back to our apartment rental in Palermo which we felt was unsafe not knowing the roads. Instead, we rented a car the day of our visit to VT and got a hotel that night in Agrigento. Yes, we double booked but it wasn't much extra money and we had a safe, leisurely time.

Wish I had known about the observatory on our recent visit to Andalucia. We landed in Malaga (after 30 hrs of flying), and needed to get to El Chorro, about 1 hr away for a hike we were doing the next day. We found public transportation in Andalucia to not always be very convenient (transfers and taking a lot of time), so we used Daytrip.com for 3 private transfers. Highly recommend!

I’m one who always rents a car. The roads from Màlaga to Granada are all highway if taking the coastal route over to Motril then up to Granada, not much different from a highway in the U.S. A more scenic route would probably be to head north toward Salinas then east to Granada.

You pretty much answered your own question. An hour taxi ride would be pretty expensive one way, let alone round trip.

If you decide to rent a vehicle, once you select a route look at the towns along it to see if anything is of interest to you. For example, if going directly north, Antequera might be a nice stop followed by a short stop to see Castillo fortaleza de Archidona. If going along the coast, Salobreña has a nice beach and once heading north, Lanjarón is nice to walk around. The drive from Málaga to Granada is less than two hours, so there is plenty of time to make a couple stops.

Looking at a couple of the roads in Google maps street view between Granada and Alhama de Granada (since I haven’t driven that route) they are definitely rural, mostly flat, but some rolling hills. In places the road is narrower and there is no panted center line. If I was driving that route, I’d stay on the 3-digit roads (A-402, A-338) and avoid the 4 digit roads (A-4151, GR-3310). The 4-digits roads are more rural, generally narrower, and have more twists and turns. There are few towns along the route. Traffic will be very light, but stay at or below the posted speed limits.

Thank you for the helpful responses!