You are in Spain. People speak Spanish. But you are also in North Africa, and many people speak Tarifit (Spanish: rifeño, a variety of Berber).
By car (or on foot)
From Morocco. Melilla is completely surrounded by Moroccan territory (and the sea), and this is obviously a very sensitive border. Many try to cross illegally into Spain, with dire consequences. Crossing legally (in either direction) is also an eye-opening experience, but presents no particular difficulties if you are not transporting counterfeit goods or hashish.
Don't forget that Spain and Morocco are in different time zones, so crossing the border into Melilla you will lose one hour, or two hours in April and May (Morocco only started to observe daylight savings time in 2008).
Air Nostrum (Iberia Regional) flies from Málaga (8 flights daily), Madrid (3 flights), and one flight from Almería, Granada, and Barcelona.
There are ferry services run by Acción Trasmediterránea.
Melilla (like Ceuta) is a territorio franco, which means no VAT or other taxes.
The city is full of cafe/bars but the liveliest part is the Puerto Noray, opposite the big Hotel Puerto Melilla and has many restaurants, bars and nightclubs. And all of the bars look out at the marina.
Melilla is a safe city to visit. There are always lots of people enjoying the beach, etc until late. a visitor who stays near the centre will not have a problem.
Walking into Morocco
Catch a bus from the Plaza de España to the Moroccan border, 2km to the south. Cross the border into the Moroccan customs and security area and line up at the police kiosk to get your passport stamped. This can take a while. Be sure to go up to the window and ask for an entry form to fill out (in French, Spanish or English) while you wait.
When you get out you will be in the village of Beni Enzar which has the port of Nador with sailings to Almeria or France, where you can find banks (just next to the port)or a collective taxi to the city of Nador. Remember to turn your watch back one or two hours!