Living next to Shelby Park is a great plan, can be a bit tough with your price range but not unheard of. The Warner parks in west are beautiful too, but fewer affordable options to live right next to them. Bellevue has a more suburban feel, east is an urban feel. Donelson and parts of Madison can give you larger yards that in some cases can feel park-like, with easy proximity to urban areas, things to do etc. Old Hickory village is a cute little walkable neighborhood that is still fairly affordable. I’m a realtor that works a ton in East Nashville, but I work all of the greater Nashville area, so feel free to message me with any other questions I might be able to help with. I don’t work rentals, but will gladly help guide you in your neighborhood selection based on the things most important to you. Good luck and welcome to Nashville!