Hello - I am looking for suggestions for a town/small city to stay where we can do day hikes of 10-15 km, easy to moderate. We plan to travel in December for 2-3 weeks. Thank you

A nice base, a small and attractive city of 41,000, would be Antequera, accessible to El Torcal Natural Park and its many dolmens. One can also access El Caminito del Rey from there.
It´s a very pleasant town with a Parador and a number of Baroque churches. It´s also noted for its Holy Week processions, which we saw a bit of last March.

More info about Antequera area hiking here and here.
And the city of Antequera here.

The city is easily reachable by high speed rail to the AVE station Antequera Santa Ana outside of town, and there is an Alamo/National/ Enterprise car rental agency at the station.

You might also look at villages in Las Alpujarras.

Grazalema , one of the Pueblos Blancos, was impressive….up in the mountains but very small, so check what facilites etc are open in December and also whether any issue with snow.
Ronda, though a city(a very beautiful ones might also work well…there’s some beautiful countryside in that wider area.

Thank you. I am going to look into Antequera. Do you know if a car is needed to get to the hiking trails?

Thank you. I will research Las Alpujarras

Thank you. I have been to Ronda, but never thought about visiting to do some walking

Yes, you would need a car for the hiking trails around Antequera, although you can reach the Caminito del Rey by train from the Antequera Santa Ana rail station. There is a thread on doing "the Caminito del Rey in winter" on the Rick Steves Spain forum, and a poster mentioned it being pleasant in February. The Málaga province in December, historically, hasn't had cold weather. And the Málaga province is nicely blessed with sun. Here's last December's Antequera temperatures.

A little bit more about Antequera here.

The Alpujarras would be a great choice for mountain hiking but my only hesitation in recommending it originally, was that it could be quite rather cold there in December, and the villages are very small, although charming. I thought of Antequera because for an extended stay, a larger town, rather than a village, would have more amenities-- large supermarkets, pharmacies, gas stations, shops for buying winter or hiking gear, more variety of restaurants, etc.

If I were the OP, I’d heed Maribel’s advice and her cautionary notes about Las Alpujarras!

Thank you for the detailed information. I really appreciate it

Well noted, thanks