Leith is good for that money – The Shore, Bonnington/Broughton/MacDonald Road kind of area is an easy walk or cycle into town. Hillside/London Road area probably good VFM at that money.
Dalry is pretty up and coming just now as is Fountainbridge. Might struggle with that money in Bruntsfield but Viewforth area would get you something good.
Lots of options, best thing is to come up and have a wander around the different areas. Buses are plentiful. Lots of good cycle paths once you know where they are.