Sicily is in a much worse place than it was 10 years ago.
Depending on how much you want "big city" experience or "smaller tranquil town" experience I would recommend Bari or Brindisi on the south east coast. I have a pet hatred of Naples because of the people there and there's nothing especially great about the city either.
In general, Italy is Italy, despite what the locals tell you. A pizza or pasta is the same in the South as it is in the North, for the most part. South tends to be cheaper as well as warmer, however has higher sexism and petty crime.
In April in the South I think you might be able to swim, depending on the weather (even if it's maybe a bit chilly!) so worth taking costumes in case you fancy a little paddle.
Trains have a bad rep, but in my experience function reasonably well and are never overcrowded. The intercity services in particular have ye olde style cabins with 6-8 seats in them which you normally have all to yourself. Use the app "Trenit" if you plan to ever get a train.
Buses turn up whenever they want. Timetables are a rough guide at best. Finding a local who speaks English is better than trying to get any sense off the bus company websites. English speakers tend to gravitate to service jobs - waiters in particular are a better bet than shopkeepers if you need to ask directions or similar.
You can function reasonably well with a few phrases:
Quanta costa? - How much?
Dov'e ...? - Where is...? (la mare = the sea, il stazione = the station, il centro commerciale = shopping centre, and so on. Just ask google translate for the names of things)
Posso...? - Can I...? (prendare = take, usare = use, pagare = pay)
Sinestra - Left, Destra - Right, Gira - turn so "Gira a destra" is "Turn right"
Halifax do a nice credit card that charges you nothing at all for foreign purchases, although it does have a small charge for cash withdrawals.
Anywhere on the coast will have a good selection of sea food, but I'd be sure of what you're going to get before ordering as it can often be difficult to tell on the menu what is fish and what is shellfish. Most established restaurants should have a menu in English.