The week of the CMA Fest (Fan Fair) is really the best week to visit Nashville because there is so much going on and it is a chance to see so many great artists at one time. I love going to the Grand Ole Opry ....there is always a good show going on and it is just such a historical amazing place. I have stayed Downtown, near the Opry, near the Airport and in Brentwood. If you are renting a car I would stay near the Opry as it is much less expensive than staying downtown and you are very close to the Opry and the Mall.
My favorite restaurants in Nashville are The Palm ( quite expensive...but a great place to go and see stars and the steak is amazing). The Pancake Pantry.....amazing Breakfast! Judge Beans BBQ.....great southern BBQ. The Wildhorse Saloon and the Honkey Tonks on Music Row are a must for first timers as there is always something going on there.
I have yet to visit the Country Music Hall of Fame but I have been a member for a while now and will be visiting this year for sure.
Other than that....I have to say that I really love taking the time and driving around the outer limits of Nashville. There is some beautiful countryside and it is just a neat experience to have.
If you have any other questions....feel free to ask.