I was hoping for some suggestions, I’ll be staying downtown first week in March.I really enjoy the rat pack era music.
Free Live Jazz at the Underground at the Mob Museum. https://themobmuseum.org/events-posts/free-live-jazz-in-the-underground-in-march/
Not sure if they are still there but the Plaza has a band that plays the "oldies". Not sure if rat pack music, might be more of the 70's and maybe 60's.
You might check out the Tuscany Hotel website, specifically the nightly schedule at the Piazza Lounge. Sunday and Monday nights should be right up your alley. Not downtown but a short Uber away and worth the trip.