These companies are a good starting point to explore hiring a car even if you are not starting your journey at the airport. They offer a selection of alternative city centre locations from where you can pick up and drop off your vehicle. Some will also allow you to pick up the car in one city and drop in another - though do check there maybe an additional charge for this service.
National (www.nationalcar.co.uk) and
To the untrained eye they are much of a muchness so I'd say your best bet is to get in touch and haggle! Have a read below of Nick Trend's tips on how to get a good deal on car hire too and you won't go wrong.
If you are staying in central Edinburgh I would suggest ditching the car hire idea. Driving in the city is a nightmare with one way systems, upheavel due to current construction of the long awaited tram line and the parking will drive you to drink and drinking and driving is a no no! Edinburgh is small, compact and easy to get around, there is an excellent bus service and black cabs can be flagged down or ordered to arrive within minutes of your call. However if you insist or are staying outside the city or intend to explore further afield then the car hire companies above can be found at Edinburgh airport and other city locations.