The cheapest parking I know of in the area would be at Union Station about .5mi away.
Parking is available in the Gateway Center Garage located under the Patsaouras Transit Plaza. The entrance is on Vignes Street. The daily rate is $6, with a 30-day limit. Payment is accepted using cash and major credit cards (Visa, MasterCard, and American Express). The parking garage is patrolled regularly by security officers.
After we set up we may find local residential parking, but I am not familiar with the area.