Borrowing on John's good data creation code and assuming the column is actually a VARCHAR instead of a char, here's a super simple way to take care of double, triple, or more words without having to know how many words there are...

Declare @address table (address VARchar(50))

insert into @address

select 'Lincoln'

union all

select 'Kentucky Kentucky'

union all

select 'Walla Walla'

union all

select 'New York New York'

union all

select 'New York CITY New York CITY'

union all

select 'Ohio'

union all

select 'Iowa'

SELECT CASE

WHEN LEFT(Address,LEN(Address)/2)=RIGHT(Address,LEN(Address)/2)

THEN LEFT(Address,LEN(Address)/2)

ELSE Address

END

FROM @Address