Nearest or next?

Nearest is the superlative form of near. It means ‘the closest in distance or time’:

We need to buy some food. Where’s the nearest supermarket? (There may be several supermarkets: which one is the shortest distance from here?)
Not: ~~Where’s the next supermarket?~~
Feeling very sick, she took a taxi to the nearest hospital.

Next means ‘the first person or thing after the present one or after the one just mentioned’:

We had the addresses of three restaurants. The first one we went to was closed. The next one was open but full. Luckily, the last one had a table free.
A: When is your yoga lesson?
B: Next Wednesday at five.