Both are in the Bay of Naples. Both are underrated. Both are better than Capri for actual relaxation.
Plan your trip →46 km². Thermal gardens (Poseidon €35, Negombo €32). Monte Epomeo. Beaches. Need 3–4 days. Stay: €70–150.
4 km². Walk everywhere. Marina Corricella is the shot. Half a day to see it; 2 days to feel it. Stay: €60–100.
Ischia: thermal therapy, beach variety, longer stay. Procida: romance, photography, intimate scale. Best: do both from Naples (Ischia 3 nights, Procida 1–2).