Frequent trains run from Palermo, Cefalu and Messina - from where you can connect to Taormina, Catania and Naples and Rome. The train station is about 3km South of the centre - buses run to the centre frequently and there are taxis.
Frequent buses run from Messina to the town centre and stop right by the passenger ferry port.
The are frequent car ferries and much quicker hydrofoils from to the Aeolian Islands (most go to Vulcano and Lipari) - lots in Summer, with fewer during Spring, Autumn and Winter and on Sundays. For timetables see SIREMAR, Ustica Lines and NGI
The centre is quite compact, so you will probably only need to walk around.
The streets around it are also attractive.
There is a very long beach there that is never too crowded. Also, there is a promenade with a nice view.
There is a car rental office in town. You can make few easy day trips to Mount Etna or Taormina. You can also take a day trip by train to Palermo (2 hrs each way)or Cefalu (1 hr each way). There is a very frequent reliable ferry service from Milazzo and the exploration of seven Eolian islands make great day trips. From the same port there are few organized boat tours to the islands. It is possible to make a day trip to Vulcano or Lipari, but you have to stay overnight on the other islands.
There are lots of small and cheap restaurants in Milazzo. Especially around the city Castle (Via Duomo Borgo Antico) you can find great places.
Il Saraceno (Via Duomo Borgo Antico, 9) offers the real Sicilian kitchen at very affordable prices and has dozens of cocktails on the menu list.
The hilltop village of Castroreale 10km away is attractive and you can stay in the Castle itself in the Youth Hostel