Just Jazz would be my suggestion. It is very new and I have not tried it. I think it's just a few blocks behind the Sahara. Check out justjazzlv.com and let me know what you think. I think it would be perfect for your challenge.
On Sundays, it's hard not to find a jazz brunch. On Paradise, Envy The Steakhouse and Gordon Beirsh come to mind. Both would be a safe bet, although they might be crowded.
If you aren't hungry, there's a little boutique on Decatur where they play very old standards. It may slower and more background music than you are looking for. The band includes Lena Primas Husband and that piano player guy from the Platters. It sounds kinda cool to sip champagne, look around, and listen to pretty music. On second thought, it might not impress a new boyfriend.<g>
You could probably find old Vegas favorites like David Van Such and The Tommy Thompson Project around town too.
Also, don't forget that we want to hear about your trip when you get back. Not so much about your new boyfriend as where you ate, the music you found, shows, hotels, etc.
And Welcome to TalkVegas.