you could try the Express by Holiday Inn, down at the Ocean terminal, Leith( Docklands area). There is car parking there, and if you need a bus there are lots of buses that stop outside the hotel that go direct to the centre in about 10-15 mins. good luck and enjoy our lovely city.
P.s there are lots of good bars and restaurants in that area, also the Ocean terminal shopping centre is across the road from the hotel and the Brittania cruise liner is docked there.