You don't want/need a car in Edinburgh and parking will be horrendously expensive. There is good public transport and a frequent train service to Glasgow. Only hire a car for days touring outside Edinburgh.
Have a look at the driving routes listed here:
Stirling and Dunfermline can be combined with Falkirk and St Andrews for a great day out.
You can also link Border Abbeys with Selkirk and Langholm.
Alternatively have a look at the itineraries listed here which will give you an idea of what can be done in 4 days.
Use this website to check on routes, distances and driving times:
Have a look at this site for more inspiration too. visitscotland.com/guide/…
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