palermo

Please get a tour book for Sicily (Lonely Planet, Rough Guide, Fodor's). It will normally have hotel and restaurant recommendations as well as telling you the sights worth seeing. On the Rick Steves tour I took, we stayed at the Hotel Ambasciatori and the area is safe and has some very good restaurants. You can also check websited like Trip Advisor to get additional info.

thank you for yr quick response, what about staying in mondello beach

Are you looking only for a beach experience or a city experience? Palermo can't be beat for the city experience. There is lots to see there. Nothing wrong with staying at the beach/suburbs, but you'll have a totally different experience than staying in the city.
https://www.planetware.com/tourist-attractions-/palermo-i-si-p.htm

We stayed in Palermo for 3 nights when we started 3 week Sicily trip. Stayed at:

https://www.laviadellebiciclette.com/en/

Excellent location in the heart of the city. Nice breakfast. And for a nominal fee they met us at the airport and after 3 flights from Canada it was welcome!

Lots to do ... for a special treat try and book an event at the wonderful opera house.

what towns can we visit from palermo , not with a car, but train or buses,joe,we have 3 full days

Cefalu, Monreale, Erice, suburbs of Palermo (Bagheria, Mondello, etc)...
Read up on Sicily on Lonely Planet and look at the Trenitalia and local bus schedules.
With only three days, I wouldn't overplan - you barely have time to see Palermo and Monreale and maybe Cefalu. You can easily spend two full days just sightseeing in Palermo proper.

Thks I hate flying but I do it , we fly from Miami to Palermo is the plane small n also the plane from Milan to Palermo