Where's your workplace? I rented a private place and also a managed apartment thru StayCity, both in Haymarket which was fine, but I needed to be near a rail station cos the gig was in South Gyle. I can give you the name of my landlady by PM.
There aren't many bad areas in Edinburgh that I'm aware of, avoid Dalry and the area around DumbyDykes road.
The Old Town is touristy and pricey, New Town is slightly cheaper but still a bit pricey (but not as nuts as London). Leith has some dodgy bits and is a bus ride out from the centre, but the Shore area is very nice and has some good hotels and flats and a nightlife to rival the Old Town. at least if you're over 30 ...
The main challenge is length of tenancy, 90% of lets are for a 6 month minimum which may not suit ... there are a couple of agencies that have some shorter term places, Edlets and Factotum spring to mind. I had a bad experience with D J Alexander, but wouldn't want to condemn them on a single cockup....
And if you're likely to be there in August, try and get something sorted in advance of the Festival, flats become rarer than hen's teeth and rents quadruple ....