Koh Samet

Minivans and buses leave Ekkamai terminal for Ban Phe pier roughly hourly and take 3–4 hours (฿200–300). From Ban Phe, the ferry to Na Dan pier takes about 40 minutes (฿100–120 round-trip) and speedboats about 15 minutes (฿200–500 per person, more for a charter). Door-to-beach from central Bangkok is realistically 4.5–5 hours.

Yes. The island sits inside Khao Laem Ya–Mu Ko Samet National Park, and foreigners pay ฿200 per adult (฿100 per child) at the checkpoint past Na Dan pier. Thais pay ฿40. Keep the ticket, it's occasionally checked. The fee is per entry, not per day, so it covers your whole stay.

Hat Sai Kaew has the widest choice of hotels and restaurants and the most going on. Ao Hin Khok and Ao Phai are the budget beaches with nightly fire shows. Ao Wong Duean balances comfort and quiet, and Ao Prao is the splurge: three upscale resorts on their own sunset-facing cove. Everything on the east coast is walkable, so where you sleep matters less than on bigger islands.

It's possible. Leave by 7am and you'll get about five hours of beach, but it's a rushed ten-hour round trip. One night makes it worthwhile, two is ideal. If you only have a single free day in Bangkok, I'd pick a closer option like Ayutthaya instead. Samet rewards the overnight, especially midweek when the weekend crowds are gone.