You need a design like this:
Table: Places Indexes:
+----+-----------+-------+------------------+ ID: Primary Key; Auto-Increment
| ID | Place | Phone | Email |
+----+-----------+-------+------------------+
| 1 | Somewhere | 12345 | test@test.com |
| 2 | SomePlace | 54321 | testing@test.com |
+----+-----------+-------+------------------+
Table: Categories Indexes:
+-------------+-----------------+ Category_id: Primary Key; Auto-Increment
| Category_id | Category_name |
+-------------+-----------------+
| 1 | Test Category 1 |
+-------------+-----------------+
Table: Category_relationships Indexes:
+-------------+----------+-------------+ record_id: Primary Key; Auto-increment
| record_id | place_id | category_id | place_id: Foreign Key
+-------------+----------+-------------+ category_id: Foreign Key
| 1 | 1 | 1 | place_id AND category_id: Unique
+-------------+------------------------+
| 1 | 2 | 1 |
+-------------+------------------------+
Then if you wanted to retrieve all the categories for place ID 1:
SELECT c.category_name
FROM categories c
INNER JOIN category_relationships cr
ON c.category_id = cr.category_id
INNER JOIN places p
ON cr.place_id = p.ID
WHERE p.ID = 1