SQL Server AS statement aliased column within WHERE statement

SQL doesn't typically allow you to reference column aliases in WHERE, GROUP BY or HAVING clauses. MySQL does support referencing column aliases in the GROUP BY and HAVING, but I stress that it will cause problems when porting such queries to other databases.

When in doubt, use the actual column name:

SELECT t.lat AS latitude 
  FROM poi_table t
 WHERE t.lat < 500

I added a table alias to make it easier to see what is an actual column vs alias.

Update

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A computed column, like the one you see here:

SELECT *, 
       ( 6371*1000 * acos( cos( radians(42.3936868308) ) * cos( radians( lat ) ) * cos( radians( lon ) - radians(-72.5277256966) ) + sin( radians(42.3936868308) ) * sin( radians( lat ) ) ) ) AS distance
  FROM poi_table 
 WHERE distance < 500;

...doesn't change that you can not reference a column alias in the WHERE clause. For that query to work, you'd have to use:

SELECT *, 
       ( 6371*1000 * acos( cos( radians(42.3936868308) ) * cos( radians( lat ) ) * cos( radians( lon ) - radians(-72.5277256966) ) + sin( radians(42.3936868308) ) * sin( radians( lat ) ) ) ) AS distance
  FROM poi_table
 WHERE ( 6371*1000 * acos( cos( radians(42.3936868308) ) * cos( radians( lat ) ) * cos( radians( lon ) - radians(-72.5277256966) ) + sin( radians(42.3936868308) ) * sin( radians( lat ) ) ) ) < 500;

Be aware that using a function on a column (IE: RADIANS(lat)) will render an index useless, if one exists on the column.

SQL Server is tuned to apply the filters before it applies aliases (because that usually produces faster results). You could do a nested select statement. Example:

SELECT Latitude FROM 
(
    SELECT Lat AS Latitude FROM poi_table
) A
WHERE Latitude < 500

I realize this may not be what you are looking for, because it makes your queries much more wordy. A more succinct approach would be to make a view that wraps your underlying table:

CREATE VIEW vPoi_Table AS 
SELECT Lat AS Latitude FROM poi_table

Then you could say:

SELECT Latitude FROM vPoi_Table WHERE Latitude < 500

This would work on your edited question !

SELECT * FROM (SELECT <Column_List>,  
( 6371*1000 * acos( cos( radians(42.3936868308) ) * cos( radians( lat ) ) * cos( radians( lon ) - radians(-72.5277256966) ) + sin( radians(42.3936868308) ) * sin( radians( lat ) ) ) )  
AS distance 
FROM poi_table) TMP
WHERE distance < 500; 

I am not sure why you cannot use "lat" but, if you must you can rename the columns in a derived table.

select latitude from (SELECT lat AS latitude FROM poi_table) p where latitude < 500