Explore the castle complex and cathedral — it's the city's top historic site with sweeping views over Prague; check seasonal opening times (often 9:00–4:00/5:00pm in November).
Leave central Prague allowing plenty of time for security and boarding for your 13:45 flight; recommended arrival 2 hours before international flights.
Board an evening EC train (approx. 5.5–6.5h) to arrive in Prague late evening — book tickets in advance and choose a comfortable connection (example departures ~17:30–20:00; check exact schedule).