Philadelphia and D.C. are worth it along with the aforementioned places. All four can be done w/o a car. And note that NOL has a trolley that runs between union station and the hotels; Alpine has hotels nearby, museum and is a small walkable town. Philly and D.C. local trains can take you to from Amtrak to hotels and from there you can walk to places of interest.
Note, for seniors, NOL trolleys are like 70 cents vs $2, Philly is free (but you have to be 65, I believe); DC has a senior card you can buy for $2 (not sure on age); NYC, Chicago and, I believe, Boston also have senior cards but I don't know the age rules. None charges for their card. Go to their transit web site for info.