Nearest is used for place. It is used to refer to people or things which are most near in space.
- Excuse me. Where is the nearest hospital? (NOT Where is the next hospital?)
- The nearest railway station is two kilometers away.
Next is used to talk about time or position in a series. It means ‘after this / that one’.
- We will get off at the next station. (NOT We will get off at the nearest station.)
- We are looking forward to your next visit. (NOT We are looking forward to your nearest visit.)
- As soon as he finished one project, he started planning the next. (NOT … he started planning the nearest.)
Next can be used for place in a few fixed expressions. In this case it means ‘nearest in space’. The most common expressions of this kind are ‘next door’ and ‘next to’.
- The boy next door is a little careless about truth. (NOT The boy nearest door is a little careless about truth.)
- Who is sitting next to Peter? (More natural than ‘Who is sitting nearest to Peter?’)