Giangilberto from Milan here. Yes — and I'll go further: for me the Aeolians are the single best thing Sicily has that most first-timers skip. But your Cinque Terre instinct is right, they are not all equal, so here's an honest ranking.
One geography check first, since you mention Erice and Marsala: the archipelago everyone means by "the islands" is the Aeolians, off the northeast coast (hydrofoils from Milazzo, an hour from your Messina–Taormina area). The islands near Marsala are a different, smaller group, the Egadi. I'll assume Aeolians — correct me if not.
The non-negotiable is Stromboli. An active volcano rising straight from the sea, and the evening boat that positions you off the Sciara del Fuoco — the black slope where the eruptions tumble glowing into the water after dark — is worth the entire trip by itself. I mean that literally: it's one of the few sights in Italy that made me forget to take photos.
Panarea deserves its own note: the smallest and the chicest, whitewashed lanes, no real cars, achingly pretty coves like Cala Junco. An afternoon and evening there, then back to base — perfect dose.
For the base itself: Lipari is the practical hub with the most life and connections; Salina is the green, quiet, winey one (capers, Malvasia, the Pollara sunset), and if I had to stay somewhere it would be Salina. Vulcano works as a half-day — mud baths and sulfur smell included in the price of admission. Filicudi and Alicudi are the wild end: beautiful, but on a first visit they're the ones I'd let go, the way you let go of a Cinque Terre village or two.
Give the archipelago three or four nights minimum — day-tripping it from Sicily wastes it. Mid-trip question back to you: how many nights can you carve out, and did you mean the Aeolians or the Egadi near Trapani? The answer changes the plan completely.