Within a ten block area we call downtown, are the biggest attractions Nashville has to offer (Take a look at my list of top walks and getting around.) But what's best for your plans - walking, Ubering, or do you need a car?
Here's my plan (and this might give you some insight since I live in the same complex as the properties.) I walk to most things downtown unless I need to get there in a hurry or it's bad weather, otherwise I'll Uber (I will NOT drive to anything downtown - waaaaay too much trouble or impossible to find parking closer than the complex.)
However, since your vacationing and have limited time, choose well between walking and catching a ride. For example, you might Uber to some areas outside of downtown and then walk once you get there to explore (see my list of neighborhoods & top itineraries.)
I hope that helps.