You are not going to get oo close to the trolly without paying weekend rates at any of the hotels. I would ck into the Hilton..it is only like 3 blocks from the port and it is right on the trolly line that goes down to the French Market and just across from the Americus Auquarium....someone else may be able to help you better.
We did the same cruise last fall and stayed on Canal St. we were divided into two groups half stayed at the Sheraton and the other half across the street at the Mariott (Ithink it was Mariott). We got our rooms on Priceline for $50 per night. The hotels were both very nice and the trolly was in the center between us.