I'm in Knoxville, but I can't imagine that the critters in Nashville will be much different than the critters here. Just about anywhere you go, I guess venomous snakes or poisonous spiders are a possibility, but I very rarely have to deal with either. Black-widows, for instance, are found in New York as well as here (although they are a different species). I have seen a few black-widows here under log piles or big rocks, but have never been bitten by one. In my mind, these things are just not anything to worry about, except to be aware that they could be a possibility if you're outside (pretty much anywhere you go).

Now, for critters in the garden, I have one word for ya...VOLES. In some areas, these pesky little varmints are a real problem. I'm sure you'll also find insect pests different here than from up in NY. However, I don't know that they will necessarily be better or worse, probably just a somewhat different mix.

I discovered I had Voles last Spring and spent alot of time setting out bait, traps etc. I think they were there the year before, but I didn't know what they were. I thought I had Moles.Will be much more observant this year.
Already put out poison bait.