NYC (with a bargain hotel - esp. near Labor Day)
Chicago
Nashville
New Orleans
Quebec
Montreal
Anything with museums, restaurants, harbor cruises, outdoor landmarks, and free concerts/festivals where babies can come and go.
Museum restaurants are often pleasant, relatively cheap, and baby friendly.
If you love theater...try switching off the baby and one parent goes to a matinee and the other goes to the evening show.
Some NYC things I did with an 8 mo infant...MOMA Target Free Thursday Eve and cafe dinner; free Fashion Institute of Tech museum to see a special exhibit; stroll Greenwich Village and go to baby stores, cupcake at Magnolia bakery, visit playgrounds; free Staten Island ferry harbor ride. We had a toddler on this trip also.