Ortigia is the ideal base for staying and visiting eastern Sicily without having to pack and unpack.
Besides Ortigia, in the new part of the city you can visit the Neapolis archaeological park, the Paolo Orsi archaeological museum and much more.

Within 2 hours by car, you can visit all the historical, architectural, and naturalistic attractions that this beautiful part of Sicily offers to its guests: 
Pantalica, Avola antica and its lakes, Noto, Noto marina, Vendicari, San Lorenzo, Marzamemi, Portopalo, Isola delle correnti and towards South Modica, Scicli, Ragusa Ibla, Puntasecca and Montalbano places.

You will find great insights by Googling the names of the suggested locations.