From a music point of view definately Heart & Soul as all the hotels are in the City centres plus you don't have any one night stop overs which are always a dash.
Think some of the hotels have been changed since i did route 66 but many where outside the city. Think Chicago & St Louis are same as Heart & Soul now which is far better, plus they have added Vegas.
Chicago - Take in a Blues Club and a Jazz Club, walkable in safe area from the hotel is "Blue Chicago" (on Clark st) its small and good but doesn't do food although next door is a cracking Irish Pub called Fado.
"Andy's Jazz Club" for another night and you can eat there.
Think you get taken to Buddy Guys or Kingston Mines on the other night in Chi-town.
St Louis - Everyone points towards Lacledes Landing (entertainment district) which is close to the hotel but to be honest when we were there was quiet.
For good entertainment suggest you check out "Beale on Broadway" or "BB's Jazz Blues & Soups" which are opposite each other and cracking places with some quality music. Both are walkable from the hotel (on broadway 400mtrs or so past the baseball stadium, its not like NY Broadway).
On another note cracking Chinese restaurant almost next to the hotel if you need a break from american food.
Memphis - You are just around the corner from Beale st, don't need to go anywhere else for food or music.
"BB Kings" is a must but can recommend place at other side of the road called "Blues City Cafe" especially if "Hillbilly Casino" or "Brad Birkendahl" are playing (both regulars).
New Orleans - Not sure best places as the Heart & Soul was my first visit and felt i just scatched the surfice (will return). Just wander the French Quarter and you'll find something.
All places i've mentioned have websites so you can do your homework as to where they are and who is playing.
Anything else please ask
Mick