Thinking of going to Sicily mid-February for around 3 weeks. Any advice would be welcome with regard to best area to base ourselves. Are there areas where the climate may be more favorable at that time of year. We aren't so much interested in the sports and the beach scene but tend more toward history, geography, restaurants - although not averse to people and scenery watching - lovely views would be nice. Should we split out stay between Palermo and an alternative. We will not have a car so public transport to other areas of the island could be a deciding factor - although short term vehicle renting might be an option.
Any advice would be most welcome.
I recommend two, perhaps three bases: Siracusa, Palermo, and another of your choice.
You will probably rely on buses. Travel in Sicilia can be slow. I am in Siracusa now, I have posted several trip reports (Palermo, Trapani, and Piazza Armerina...).
I would definitely not want to choose just one base for three weeks in Sicily. I'd want at least three and would prefer more since transportation tends to be slow and there are very few buses on Sundays and holidays. You'll end up using buses a lot because of limited rail service.
Siracusa was my favorite place and it's good for visiting the Baroque towns in the SE, so that would be a definite stop for me. And
Palermo because of the large number of sights there (though some folks find the city overwhelming). After that, you have to look at what you want to see. Catania/Taormina/Mt. Etna are one cluster. The interior has Enna/Piazza Armerina/Caltagirone/Villa Romana del Casale/Morgantina. Then there are the Greek sights in the south and southwest. And Trapani/Erice in the northwest. And on a trip of that length I'd consider the Aeolian Islands, but verify that they are not dead at that time of year.
Check temperatures for the time you plan to visit. Your passing reference to beaches concerns me, because I think you may be expecting warmer temperatures than you are likely to encounter.
We are doing the Rick Steves Sicily tour this October, but I have some friends that also did it this past February. They said the weather was really nice and they enjoyed it. Take a look at the tour itinerary for some ideas of locations and things to do:
https://www.ricksteves.com/tours/italy/sicily
As to climate, Sicily is a sub-tropical climate, not tropical. The weather that time of year varies, lows into the 40's, colder in the mountains. There is no beach scene in February and many resort hotels and/or restaurants may be closed.
If renting a car, do so before or after your stay in Palermo. I would strongly advise against driving and/or parking in Palermo. Traffic is extremely heavy and hectic and there is next to no public parking.
Other posters have given good advice regarding where to stay and transportation.