There is a nice Marriott at the airport that is literally a chip shot (okay, maybe a 6 iron) away from the airport car rental places. The Edinburgh airport is 8 or 10 miles west of downtown, so you would have to either bus or taxi to downtown to run around down there, but it sounds like from your agenda that Edinburgh is not where you are going to be spending much time. If it is you would be better off staying near downtown somewhere and walking or taxiing most places rather than worrying about trying to drive and park a car in Edinburgh. Then when you are ready to leave Edinburgh go rent your car for the rest of your trip.

My wife, infant son and I stayed at an apartment hotel called EQ2 which was less than a mile SE of the castle, well within walking distance of most of what you would want to see, and on a quiet waterway (right at the dad end of Edinburgh Quay) where we could see canal boats, ducks, ans swans out our window. It was definitely cheaper than staying at one of the bigger downtonw hotels, and had plenty of room with a separate bedroom, living room, and kitchenette with mini laundry. Several decent restaurants nearby. A bit off the beaten path, but not so far that you felt isolated. We had a rental car for the week we were in Edinburgh and 5 additional days we were travelling the central highlands, but we really did not use the car at all in Edinburgh---it sat in the hotel garage. Too complicated to drive and too hard to park in town, especially when you have to drive on the lefthand side of the road with a righthand drive car (the reverse of the US).