Nashville 1st time
You've gotten some good reccomendations - I second City House & Margot, for sure, as well as Monell's. I'd also add Flyte (just up the road from Arnold's, but a world away) for a great, interesting wine list and really good creative new American cooking. Go to Leon's on 2nd for pralines and caramels - you won't be sorry! Also, if it is hot (and in August, it will be) go have a popscicle at Las Paletas in the 12South neighborhood. If you have an inkling that you want BBQ, drive to Nolensville for Martin's. You'll wait, and they may be out of dessert (go early - they close early, or when they run out of meat) but it is good.
I also live in NYC and just visited Nashville this past weekend (here's my trip report). You have to go to Monell's. NYC attempts at southern food can't get close to Monell's. Loveless was worth the wait though I don't think I would go back on a day where they don't offer chicken fried steak (it's the blue plate special on Saturdays) since I think their other breakfast dishes (like just regular eggs and bacon) are just okay.
Stay away from seafood and steakhouses. You will not find anything in Nashville that rivals what you can get in New York. Unless you mean catfish, and in that case, Arnold's serves some mean catfish - on Fridays, I think. Go to Arnold's, regardless.
Go to Prince's Hot Chicken.
Go to Watermark.
Go to Hog Heaven.
Go to Pancake Pantry.
You can search Nashville on this board and find lots of recommendations.
Here are some recommendations; don't know if you have a transportation or not, but Nashville's a car town -- everybody drives everywhere.
Anyway, some recommendations:
Margot Cafe & Bar -- ranks in most Nashvillians' top 10; located in East Nashville at Five Points, minutes from downtown
City House -- rustic Italian in Germantown, also minutes from downtown. Tandy Wilson is the chef/owner; great guy, great chef, always creative, fun room
F. Scott's -- in suburban Green Hills, adjacent to Green Hills Mall; don't worry -- excellent food, outstanding wine list, excellent service -- probably lands in the Top 5 for most foodies in Nashville.
Zola -- just off West End Avenue near Vanderbilt; chef-owned restaurant -- interesting menu -- been around for years and great food.
Park Cafe -- on Murphy Road off West End -- just a few blocks west from Vanderbilt. loyal customers swear by it; my neighbor treats it like his personal commissary. Great food, solid service; enjoyable neighborhood restaurant.
Others, I am certain, will provide additional comments.
Lunch Monday-Friday -- a taste of Nashville -- go to Arnold's on 8th Avenue, near downtown. Down home, Southern-style meat 'n' three -- James Beard Foundation recently named Arnold's an "American Classic." If you go once, you'll probably go twice while visiting. Warning: no health food served, skip breakfast for sure, might not want dinner later.