How to set variables to multiple values (that are integers)?
You can use a table-valued parameter.

CREATE TYPE dbo.Facilities AS TABLE
(
  FacilityID TINYINT PRIMARY KEY
);


Then your stored procedure can say:

CREATE PROCEDURE dbo.whatever
  @FacilityDivisionID TINYINT,
  @Facilities dbo.Facilities READONLY
AS
BEGIN
  SET NOCOUNT ON;

  SELECT ... FROM dbo.wherever AS w
    INNER JOIN @Facilities AS f
    ON f.FacilityID = w.FacilityID
  WHERE w.FacilityDivisionID = @FacilityDivisionID;
END
GO


Then you can call it from T-SQL like this:

DECLARE @t dbo.Facilities;
INSERT @t VALUES(1),(2),(3),(4),(5);
DECLARE @d TINYINT = 6;
EXEC dbo.whatever @FacilityDivisionID = @d, @Facilities = @t;


Or from C# using a DataTable and a parameter type as Structured. You can search to find plenty of examples of using TVPs from application code.