What to do between sidewalk and curb?

Why not just check out what others in the area have done, pick out what you think would work for you and go from there.

Personally, I'd just let grass grow and mow/trim it when needed. That would be over and done with in about 5 minutes a week.

Why not grass?

Yeah that pic is probably somebody who pays someone else to keep up their landscaping. But for OP with his 3'x50' strip, he can just set his mower height higher and trim it all at once. That's if he wants something besides grass, which is probably the best option. But he was asking for other ideas

Doesn't get a lot of sun.
Does get a lot of foot traffic and sounded like a future mud hole?

Landscaper just suggested jasmine.

Thanks.

FYI was redoing my driveway post IDA from a combination of the neighbor's old tree causing cracks and Entergy trucks putting in some work on my apron. Wife wanted to look into adding a circle driveway and limestone to add some additional off-street parking. Jefferson Parish nixed the idea because of the location of the utility pole and warned her that if we want to do anything other than grass, we need their approvals. Then immediately said they would deny anything other than grass.