How to insert into TABLE Variable?
Use this one:

DECLARE @coordinates TABLE (
    latitude1 DECIMAL(12,9),
    longitude1 DECIMAL(12,9)
) 

INSERT into @coordinates
SELECT
    latitude, 
    longitude
FROM loc.locations 
WHERE place_name IN ('Delhi', 'Mumbai');

SELECT * FROM @coordinates


Note:


You created 4 column with NOT NULL behaviors, but your inserting on 
2 columns only. It will return an error.
Use INSERT INTO instead of SELECT INTO. Table is already created.
Use SELECT..FROM when calling DECLARE tables.