I'll second the vote on the Renaissance. Great location within walking distance of a good number of music venues and right in the heart of downtown.
As far as what to see, I'll leave that to others. I last visited Nashville to spend time with friends and didn't do much touring.
I would echo the thoughts about the Renaissance. It is within walking distance to most major attractions (Ryman, Country Music HOF). I would also recommend taking in a show at the Opry and taking the time to do the backstage tour after the show. In terms of restaurants I would recommend the Pancake Pantry for breakfast (near the Vanderbilt campus) and Puckett's Grocery for any meal. If you have a car and are looking to get out of Nashville for a few hours there is a quintessential small town (Franklin) about 30-40 minutes south with a Puckett's Grocery and some neat small shops.
The CY is a short walk to a lot of places and is usually less expensive than The Renaissance. If you don't mind driving the RI near the airport is very comfortable as well.
Shopping at the outlet mall is near and their are a lot of nice places to dine near the RI as well.
One thing that amazes me is how the music goes on in Nashville all the time. It is a very enjoyable place to visit.
Living only 100 miles from Nashville, I don't often stay overnight, but my son went to college at Vanderbilt, so I stayed at Hampton Inn or Marriott near the campus most of the time. If you have time to walk through the campus it's a treat to do so. Stop by San Antonio Taco, near the campus for lunch! Of course, the Opryland Hotel (on East Side) on beltway is a fabulous place to stay, or just to walk through,or have lunch. Grand Ole Opry Theater is nearby also. The Opry is the longest running, live, radio broadcast program in the U.S. - A must see even if you aren't a country 'n western music fan.
The Hermitage - Andrew Jackson's home (remember ,the hero of the Battle of New Orleans) - is only a short ride from downtown Nashville, and close to the Opryland Hotel.
Green Hills Shopping Center (indoor shopping) is South of Vanderbilt campus and a few miles North of Franklin, mentioned by others.
It's not in Greece, but you can still visit the Parthenon. Nashville has one that looks like the original. There is a Marriott next store to the Vanderbilt football stadium. It's a very nice hotel. If you get good weather for your March weekend, the park across from the Marriott is full of plants and nice walking trails. If you're a hot dog lover, try Cori's DogHouse..a short walk from the Marriott.
We stayed at the Union Station this past weekend. A different feel from standard Marriott's as this is an old train station with a grand lobby. It's not quite as close as the renaissance or CY to downtown but still walking distance. We visited the Frist centre next door. The Capital Grille and Merchant's are 2 non-chain options for downtown Nashville restaurant s
I recently stayed at the Renaissance in Nashville in mid-January. It was a nice property and within walking distance to key night/entertainment spots like Ryman (which is a must visit for the Grand Ole Opry though I believe its season has ended and it is now playing at the Grand Ole Opry House, which is located a few miles outside of downtown). Unfortunately, the room rates are high and the concierge lounge was, at least in January, under renovation and had been relocated to a boring banquet hall room. I personally felt that were lots of areas to explore in Nashville so having a car was valuable and thus staying outside of downtown was okay.
For food, I enjoyed Husk, The Catbird Seat and Jeni's Ice Cream (based out of Ohio).
The Gaylord seemed different and potentially fun, but it was also quite touristy and overwhelmingly busy due to many conventions going on simultaneously at the attached convention center.
Renaissance hands down if you want to be in the middle of all the action. We always stay on points so I can comment on rates. Also have stayed in the Union Station, pretty cool but not too quiet at night, thin walls if you know what I mean. The CY by Vanderbilt I hear is nice but not a short walk and definitely not at night.
Definitely get a car though as there is plenty to get out and see (many highlighted in this thread, Franklin is a must). I also HIGHLY recommend Pharmacy Burger (across the river, google for address). Great burgers, sweet potato fries/tater tots and excellent craft beers. Music row, Belle Meade Plantation for some local history ( Belle Meade Plantation ) The Gulch area is fun also, good whiskey bar . Lots to see and do in Nashville..
I am a big fan of the Gaylord brand because there is so much to do right within the resorts. Nashville has the Nashville Hotel | Gaylord Opryland Resort & Convention Center and you will find entertainment and dining right within the resort. Of course, when in Nashville, the Grand Ole Opry is a must, and if you are a Johnny Cash fan like I am, you would not want to miss the Johnny Cash museum The Johnny Cash Museum and Event Space. Hope you have a great time.
I saw the Charlie Daniels Band, Gloriana, and some others when I was in Nashville (May 2012). The Opry was an experience I would recommend to any music fan. I would also highly recommend the backstage tour.
My son lives in the Nashville area. A backstage tour sounds like a great idea. It would be great fun to take my son's family. I am sure the grandkids would love it.
We have stayed at the Renaissance and it was located in a great location. It's across the street from the Ryman and easy walking distance to the honky tonks. Our room was clean and we didn't have any issues when we were there.
If you are only visiting areas downtown, then you probably don't need a car. When we were there, we were using Nashville as a center point for other items outside of Nashville (e.g. Grassmere Zoo, Jack Daniels Distillery).
Another great sightseeing venue for history buffs is The Hermitage, which is Andrew Jackson's home. Fascinating property, knowledgeable docents, and an Andrew Jackson impersonator who walks the grounds and responds in character -- really well done. Go to www.thehermitage dot com to learn the details.
Last visit, we stayed at the RI on the eastside of town. Belle Meade plantation is worth a visit, a side trip to Jack Daniels distillery was fun, downtown is worth a look for sure, and check out concerts at the Grand Ol Opry--even if you think you don't like country music. Last time we attended a benefit at the downtown concert hall and it was the best concert we have ever seen--a diverse group of musicians, who played as a group at the end. Check trip advisor!
Many have posted sound advice in reply, but I'd like to mention two properties in the Nashville area that haven't been mentioned - the Nashville Airport Marriott and the Franklin Marriott Cool Springs. When needing to visit the Nashville area, I always look to stay at the Airport location. It seems to be less expensive than the Renaissance and I enjoy the location away from the bustle of things. While the location is near the airport, I have not been noticeably frustrated by noise. While you won't have trouble seeing the hotel (it's on a bit of a hill), knowing how to get there can initially be a challenge. I suggest a GPS or good directions from someone at the hotel.
In addition, you may want to consider the Franklin Marriott Cool Springs. I have enjoyed this hotel which is a bit away from Nashville proper and its bad traffic. It's a very nice place and is convenient to sites south of Nashville. Huntsville, AL and its Rocket Center and Space Camp are not very far down I-65.
You could also drive north a bit into Kentucky and visit the Corvette Plant (with production tours, Bowling Green), the Corvette Museum (Bowling Green; www.corvettemuseum.org), Mammoth Cave (the world's largest known cave, near Park City; www.nps.gov/maca/) and the eight distilleries on the Kentucky Bourbon Trail (various; kybourbontrail.com).
So if you need to be downtown, try the Renaissance and/or the Vanderbilt Marriott. But if not, you may want to stay at locations out a bit and possibly visit some nearby sites.