The pentland hills are 5 minutes walk from our house, these give you great views of edinburgh and the Forth. There are also mountain bike tracks, various walks around the Pentlands as well as opportunities to fish in the reservoir.
There are two buses that terminate within 10 minutes walk of the house both of which take you into the city centre (25 minutes) and all the way to Leith (stops beside ocean terminal and the Royal Yacht Britannia). In Edinburgh there is the castle, the parliament buildings, Holyrood palace, Arthurs seat, various museums, historic buildings and art galleries.
During most of August Edinburgh hosts the Edinburgh Festival (https://www.edfringe.com), with thousands of comedy, music, plays, theatre etc products at hundreds of venues alongside street performers.
The Edinburgh Tattoo which takes place outside the castle and hosts military bands from the Uk and abroad (https://www.edinburghfestivalcity.com/festivals/royal-edinburgh-military-tattoo)

Our house is also only a few minutes from the edinburgh ring road and in an hour you can be in Glasgow, Stirling or Perth. There are various castles within an hour of Edinburgh (Stirling, Craigmiller, Tantallon, Blackness, etc)
Various beaches are within and hour driving distance with Gullane, North Berwick and Aberdour popular.