If you wish to escape the city for a bit, our ultimate recommendation would be to visit North Berwick. North Berwick is a Scottish seaside town, only a 30 minutes train ride away from Edinburgh. In the nineteenth century it became a popular holiday destination, due to its sandy beaches. The town itself is home to a variety of quirky little shops and a Seabird Centre, where you can also book tours to the nearby Bass Rock. And believe me, Bass Rock is an absolute MUST for anyone who loves wildlife.
If you want to read more about North Berwick, how to get there and what to do, we wrote a seperate post about it: North Berwick – Daytrip from Edinburgh.