Oh, no…why are you traveling to Edinburgh by car. You are going to make your life very hard you know. Avoid it at all costs.
Parking in Edinburgh is a nightmare and expensive. Our best recommendation is to park at the park & ride bus stations on the fringe of the city and catch a bus back in.

Park & Ride
They are safe and free, so you just pay the bus fare. We suggest the Islington Park & Ride which is near the airport, and catch bus 48 or X48 to the hostel.
Otherwise, you will have to pay for parking usually. The streets have free parking after 7pm at night usually, until 7am, but you must never test the parking inspectors. They are a private company that will book you if you are one minute late. If you want to park in a secure undercover car park, it will cost about £20 overnight. Street parking usually costs from £1-£2 per hour.
More information about parking from The City Of Edinburgh Council here.