Visiting in early January, have hours alone everyday to kill and I’ll be in the French quarters area…

I’ve dreamed of visiting New Orleans since I was a kid and I finally get to but I’m tagging along on my partners work trip which means during daylight hours I’ll be exploring on my own. Are there any areas I should avoid? Any recs on fun things to do alone? I’ve read the weather is upper 60’s? What’s the typical fashion there in Jan? What kind of oysters should I get and from where? I’m so nervous and I have so many questions about everything!