I totally agree with the Harry Connick vote - in particular, "To See You."
If you really like Norah's album, you owe it to yourself to check the back-catalog of her guitar player's solo releases. Jesse Harris is the name, Jesse Harris and the Ferdinandos is the band.
"The Secret Sun" has Norah guesting, so you'll have a tie back to her music as you branch out. =)
You can find original recordings of "I've Got to See You Again" on their CD "Crooked Lines" and while I don't want to burst anyone's Norah-bubble, "I Don't Know Why" first appeared on the Ferdinandos' eponymous debut. (sample:
http://www.jesseharrismusic.com/audio/dont-know-why.mp3)
It's not the lush productions you hear on Norah's album, but it's some really heartfelt music and amazing songwriting.
If you're looking for instrumental jazz with that kind of feel, any of Joshua Redman's late-model recordings are all excellent. Moodswing is still my favorite...