Corfu

Yes — it's the better of the two fortresses for a cruise day. The Old Fortress sits on a rocky promontory at the east end of the Spianada esplanade, and the climb to the lighthouse at the top gives you the best view of Corfu Town and the Albanian coast across the strait. Summer hours (April–October) run 8am to 8pm with last admission at 7:40pm; winter hours (November–March) are 8:30am to 3:30pm. Tickets are cheap (around €6 general admission). The New Fortress on the other side of town is also open but smaller in scope — pick one if you only have a few hours.

Comfortably, yes. Achilleion is about 10 km south of Corfu Town in the village of Gastouri — roughly 20–25 minutes by taxi (€20–25 each way) or a Blue Bus No. 10 ride from the city center for under €2. It's the 19th-century palace built for Empress Sisi of Austria, with the famous Dying Achilles statue and gardens looking out over the Ionian. Open 8am to 8pm in summer, 8am to 4pm in winter, €7 general admission. Allow 90 minutes on site. A morning Old Town stroll plus an afternoon Achilleion run is a realistic cruise-day plan if your ship is in past 5pm.

Only if you've been to Corfu Town before, or if your ship is in past 7pm. Paleokastritsa is the famous beach village on the west coast, about 25 km from the port — 40 minutes each way by taxi, longer by Green Bus. The water is the kind of clear-blue that makes people post about it, and the cliffs are dramatic, but you'll burn three hours in transit and miss the UNESCO town that's a 25-minute walk from your ship. If it's your second Corfu call, swap the town for Paleokastritsa. If it's your first, save it for a return trip.

Very safe by Mediterranean cruise-port standards. Corfu has one of the lowest crime rates in Greece — violent crime targeting tourists is rare, and the petty crime that exists is concentrated in summer high-season crowds in the Old Town and on busy beaches. Standard precautions apply (bag across chest, phones out of back pockets in crowded alleys), but the constant-vigilance posture you might take in Athens or Naples is overkill here. The seaside walk between port and Old Town is well-lit and busy throughout the day.

Greece is on the euro. Cards work in restaurants, museums, the Achilleion ticket office, and most taxis — contactless is normal. Carry €30–50 in small notes for the Blue Bus (driver gives change but exact-ish helps), neighborhood tavernas in the Old Town's Campiello quarter, and tipping. ATMs are on every other corner in the Old Town; use bank-branded ones (Alpha, Eurobank, Piraeus, National Bank of Greece) and decline the dynamic-currency-conversion offer at the screen.