I don’t think such a place exists in Edinburgh, at least not in the city unless you can spend gazillions on an apartment. Parking is heinous everywhere.
If you need to get out of the city by car for work definitely south side – the north is all hemmed in by the firth of forth and you then have to cross the whole city to escape it.
Don’t be tempted by the partial gentrification of Leith – it remains a shithole. (sorry but is true I lived there for 6 months) and the traffic to get out to the A1 is always bad.
With that budget for rent you could get a decent place in Morningside or Bruntsfield way, not too studenty and decent bars etc, fairly quick exit to the A720.