You'll need at least a three-night stay for a proper introduction to Malta and a week to 10 days to become well-acquainted. Where you stay is a function of how long you stay, as well as your personal preferences and interests. My own ideal visit would start with a few days around Valletta, then continue with four days to a week on Gozo or Comino.
Malta: Unfortunately, most hotels here are in congested, touristy areas, and few offer any sense of place. The style, decor, and British Empire patina of the conveniently located, 130-room Phoenicia wins our vote. Two oceanfront hotels in swishy St. Julians, the Westin Dragonara (310 rooms) and Radisson Bay Point (252 rooms), offer sparkling new facilities but a decided lack of character.
Gozo: For an extended stay and immersion into local flavor, I'd settle into one of the antique "character" homes available through Gozo Farmhouses. These vacation homes, Gozo-style, have been thoroughly modernized and feature comfortable, up-to-date, rustic furnishings. Most have scenic terraces and private pools. You'll need a car for shopping and exploring (rentals are cheap), but no foreign language proficiency; English is the official language.
If I were staying only a few nights, I'd opt for the elegant Hotel Ta' Cenc (pronounced Ta Chench). Rooms, suites, and a few villas are available in low, sandstone buildings set along the contours of a dramatic cliff-top.
Comino: If you really want to get away, stay in the quiet bungalow section of the Hotel Comino. Set on a point overlooking the bay, the bungalows afford a spacious, viewsome private perch. Lunch and dinner, served buffet style, will be at the main hotel.