In early May last year I took a public bus to Capileira (in the Alpujarras beyond Pampaneira) and then walked downhill to Bubion. I think going on down to Pampaneira on foot would have added a lot of walking time because the road is very windy, but I notice the town of Capileira looked very attractive--and larger/livelier than the other two--as the bus took me back to Granada. So under normal conditions, I know there's bus service that makes a day-trip to Pampaneira very possible; it's not terribly frequent, but it's usable. As always when researching transportation schedules (and especially with buses, which often are infrequent even on the busiest days), you must pay attention to the day of the week; schedules can be very different on weekdays vs. weekends, not least because some buses are scheduled for the convenience of commuting workers and schoolchildren.
I don't know how taxis feel about making the long trip between Granada and Pampaneira, but I imagine there is some demand for that service; I believe a good number of European tourists probably go hiking in the Alpujarras, and most likely not all of them want to rent a car. Keep in mind that, though the distance is just 44 miles, you'll be paying for 88 (presumably twice), because the taxi will need to return to its origin after dropping you off. I found these taxi companies (probably all based in Granada) listed on the Rome2Rio website (whose information I absolutely am not vouching for):
Taxi 7 Plazas taxi7plazas.com PHONE +34 608 45 54 63
Granada Taxi granadataxi.com PHONE +34 958 28 06 54
Big Taxi Granada bigtaxigranada.es PHONE +34 639 584 754
A plus for visiting one or more of the towns in that area is that they are at (moderate) altitude and likely to be not as hot as the rest of Andalucia at the time of your trip.
This is a situation in which I'd recommend Googling photos Pampaneira, photos Ronda, etc., to get an idea of which places offer the sort of surroundings you're looking for. The most picturesque views/architecture tend to make it onto the internet, so if the pictures don't especially entice you, you can be reasonably sure that the place will not be more appealing in person from the visual standpoint; obviously, it might have other features to recommend it, such as a lively atmosphere. One thing I try to pay attention to is whether the vast majority of photos are of one spot/view; I prefer to head to places with decent-sized historic districts as opposed to (for example) just one spectacular building or square.
Edited to add: Nick recommended Carmona while I was writing my post. I considered mentioning it myself but thought it might not be hill-towny enough for you. But I think Carmona's very attractive. It's only about 22 miles from Seville and has relatively frequent bus service.