If you want walking distance, your options are the Hampton Inn Vanderbilt, Hampton Inn Elliston Place, Holiday Inn Select Vanderbilt, Marriott at Vanderbilt, Courtyard Vanderbilt, the Hutton Hotel, Loews Vanderbilt Plaza and Hotel Indigo. All are within about 1-2 miles of Centennial Park.
Pretty much anything with "Vanderbilt" in the name is going to be close to the start and safe.
Also, April in Nashville is very screwy. A few years ago, it was near freezing...and last year (or this year, I can't remember), there were people having heat exhaustion.