The phrase "approach the nearest" is correct and usable in written English.
It can be used when giving directions or suggesting someone to move towards the closest location or object.
Example: "If you need assistance, please approach the nearest staff member for help."
Alternatives: "head to the closest" or "move towards the nearest".
When a doctor determines the need for a transplant, patients generally approach the nearest medical center that performs the operations.
He was fighting, he told her, in a "beautiful war," and he was on the side of the realists — those who believe that "we are the most successful in art when we approach the nearest to nature and truth".
A farmer could sell his crop to a private trader, but for many small tillers, it was far easier to approach the nearest government granary, and accept their rate.
One may approach the nearest primary health care center where he/she lives ; they are not accepted in any other one but sent to their respective region's primary health care center.
Approach the nearest women's welfare organization in your city/town if you are being raped or molested at home.
With this approach, the near-tip non-singular stress field can be accurately evaluated by direct use of regular numerical methods such as finite elements.
Furthermore, as the wild-type kinetics speed up towards extreme membrane potentials, they typically seem to approach the near-constant value of I126F.
She approaches the nearest border official.
He checked out Manhattan restaurant menus and, if they served crab, approached the nearest Spanish-speaking worker.
A man emerged and started approaching the nearest group of players, who were engaged in an exercise that seemed to me like a recipe for concussions.
We approached the nearest pair, who were perched at a discoloured bench with a chess board between them.
