Bed and Breakfast In Edinburgh

http://www.visitscotland.com/accommodation/bandbs/edinburgh-lothians/
this link should help you choose somewhere.
Look for somewhere that you can park the car for free , Edinburgh and cars do not mix very well and a car is useless to you to visit the sights in the city. However Edinburgh does have an excellent bus service which is cheap and very efficient(day ticket £4).
As to where to stay, that's difficult and if you let me know what direction you are coming from in the car I can maybe help.
A favourite area for B&B is the Newington area of the city specifically Minto street,Newington road, Mayfield Gaardens and Craimiller park (all one long road ) there are numerous small hotels and B&B's in and around this area,furthest point is about 2 miles from the city centre and there are numerous buses that will get you into the city in 10-15 minutes, you should never have to wait more than 10 minutes for a bus.

This is the B&B we stayed in back in October. http://adriahouse.co.uk/ The staff is extremely friendly, helpful, and cheerful. They provided great advice and were flexible with the room. We were on Skye and had to leave a day early due to weather and the Adria House folks took us a day early and arranged things such that we didnt have to change rooms. The breakfast was great and they packed us a carry out breakfast on the morning we left for the US. Our room was huge! They are within walking distance of the Royal Mile area and close to the last stop (Prince Street) of the tram from the airport. If you are walking from the tram with your luggage the first trip is a bit of a climb as they are up a hill but as you will see much of that end of Edinburgh is hilly. I'd stay there again in a minute, we really enjoyed the place. We did not request an "ensuite" bathroom but there is absolutely no issue with privacy..give them a look if they are in your price range. You should ask about parking as we did not have a car so didnt we didnt have to navigate what appeared to be a pretty challenging driving experience in the city of Edinburgh. We drove in the highlands but the city would have pushed me to the limit. We left the car at the airport and took the tram into the city.

I stayed in the Kew House B&B a couple years ago and it was fabulous. The location was really good - about a block from Haymarket train station and on a major bus line. The city center is within easily walking distance and they do have car parking for guests. They are on the higher end of the B&B spectrum but they really earn it.

We've booked this one this May: Priestville Guest House - http://www.priestville.com. I talked to Colin and he was very kind & helpful...and it's very reasonable with full breakfast...
Jean

Thank you for your replies! They have been quite helpful!

we also booked at Priestville Guesthouse. Colin was super accomodating, the rooms were big for just two of us (though it is a shared bathroom) and the breakfast was probably one of the best Scottish breakfasts we had.

My daughter and I also stayed at Kew House last summer for 4 nights after reading a recommendation on this site. It was lovely. The owners are wonderful and we enjoyed chatting with them. They also gave great recommendations for things to do in the area. I can't recommend them enough. I would love to stay there again. It is an easy cab ride from the train station and easy walk into the city.

I'm booked for 4 nights in May at the Hedges. You might take a look at it, especially about parking. I dealt directly with Heather Macdonald there, but I won't have a car, so I have no clue about that. It seems like a good deal for me as a solo traveler and the breakfast looks great.