Some modal verbs of obligation or necessity include must, need to, have to, don't have to, needn't, don't need to+infinitive. There isn't necessarily only one correct answer for each one. In other words, there is more than one correct answer since they are used for obligation or necessity. I have included all of the appropriate choices.
1. You need to get a visa when travelling between EU countries.
- You could also use must or have to.
2. The cabin crew of an aeroplane must check the passengers have their seatbelts fastened before take-off.
- You could also use need to or have to.
3. First class travellers don't need to worry about small uncomfortable seats.
- You could also use don't have to or needn't. Note that needn't isn't a very common word to say.
4. If you're travelling to an area with tropical diseases, you have to have vaccinations.
- You could also use must or need to.