It really depends on what you want out of the neighborhood. Uptown/Turtle Creek are great areas and will have a few smaller properties scattered in it but predominately will be the larger/high-rise complexes you are trying to stay away from. If you would like close proximity to those areas but more of a smaller community or garden-style feel try the Knox Park and Knox / Henderson areas to stay close to Uptown / Turtle Creek. Or venture out a bit and look into Lakewood, Oak Lawn or White Rock to get the fun, funky and more intimate type of apartment homes that you might be looking for.
Let me know if you would like some help looking into those. I know of some great properties that can offer that change of pace if that is what your truly looking for. Hope this helps!