My two sisters and I, all of whom are btwn 22-27, are planning to go to Sicily the first week of June. We will only be there for four days so I'm thinking we only really have time for one town. I could really use a recommendation for which town we should stay in, keeping in mind that we want to spend time at a beautiful beach and at the ruins. At this point I am really torn btwn:

Palermo/Mondello
Taormina
Cefalu
Lipari or one of the other islands

Anyone have any suggestions for which town and, if so, what hotel to stay in when we're there?

Thanks ahead of time!

I would do Taormina but also include a stay down in Siracusa (actually Ortigia) for a magical stay in Sicily!

Try something different and consider – Agrigento. It is city on the south coast, classic Greek ruins, and beautiful beach.

Agrigento.

I agree. If you are after beaches and ruins within easy reach of each other your best bet is Agrigento/San Leone.
San Leone is a lovely seaside resort literally touching Agrigento.