If you visit in summer, the Botanical Gardens in Edinburgh are lovely and there is also a very nice cafe there called the Terrace Cafe. I don't know if your level is enough to read books in English, but there is a heavenly small bookshop nearby
<a href="https://www.heraldscotland.com/news/17639368.the-little-shop-that-could-the-golden-hare-books-in-edinburgh-wins-bookshop-of-the-year-award/" target="_blank">https://www.heraldscotland.com/news/17639368.the-little-shop-that-could-the-golden-hare-books-in-edinburgh-wins-bookshop-of-the-year-award/</a>
There is always something of interest on the Royal Mile just in terms of atmosphere. If you can afford it the open top bus tours are nice because you get to hear commentary on the places you go past, but if you are short on money maybe it's not worth it. If you like zoos Edinburgh Zoo is in Corstorphine which is only about 3.5 kilometres from the centre by local bus, not too long a journey.
I looked today for a hotel price in mid-August when there is a concert I'd like to see (Sharon Van Etten) and the price was over £150 - it seems the accommodation prices go crazy when the Edinburgh Festival is on. So unless you have specific things you want to see at the Festival you can save a lot of money going at a different time of year.
I agree with the suggestion of taking a one-day minibus tour with driver guide leaving from Edinburgh and returning the same evening. I haven't done one myself but I have heard good things about Rabbie's Tours.
I am from Glasgow, so if you have questions about modern Scottish life feel free to ask. Unfortunately I am more interested in Spanish culture than my own, shame on me, so I don't know much about tartans and whiskies and things like that.
Have a great day!