Lanzarote is a great place to go in October- guaranteed warmth. The people are very welcoming and it feels safe. Peurto Del Carmen is one of the nicest regions I have been to. Hope you have fun wherever you end up !
Keep an eye on package hols as the summer timetable changes around then - you may get to the hol. but have a problem getting back as the timetable changes. Decent package operator will advise, or do look at putting your own tour together - easy enough and gives you lots of options to do what you want.
Cyprus, Crete, Canaries, Morocco, and possibly Malta, Sardinia, Tunisia are options.