We intend to buy tickets for the castle. Is it easy to visit without a guide? Also, after the castle can we tour the city on our own? Any suggestions on sights?
We did. Just walked up to the ticket office and buy the ticket. There is a lot to the castle and in hindsight a guide probably would have been useful. A lot of time consumer signs to read. Hollyrood (sp?) at the other end of the Royal Mile is worth the time and even the parliament building was interesting.
It's very easy to visit & enjoy Edinburgh Castle without a guide. There are plenty of informative signboards as well as docents and costumed interpreters in various spots. The castle is huge, so you can easily spend a couple of hours and still not see every detail.
There is often a sizeable line at the ticket windows. If you don't buy ahead, at least look it up online and decide ahead of time whether you want the regular ticket, senior, any children, and/or some type of combination ticket. That way you can tell the agent exactly what you want instead of having to run through a range of options.
I visited Edinburgh on a very long day trip from London and got right on a HoHo bus at Waverly; good way to see various areas and I exited at the Castle, which had a long line for tickets (I was there in mid-August), even though I had a voucher and there was a separate line for that. I spent 2-3 hours touring it without a guide, then walked down and explored the Royal Mile area, had lunch in a pub and shopped a bit, then back on the HoHo bus to see more of the city.
I visited Edinburgh Castle on the Rick Steves Tour. We had a guide who gave us the highlights, then we had time on our own to wander around the castle area. Yes, it easy to tour it on your own. I agree with getting tickets ahead of time if you can. It can get quite crowded. Absolutely you can tour the city on your own. Get a map and check online to see where you want to go. Holyrood Palace at the other end of the Royal Mile is definitely worth it, especially if you like Mary Queen of Scots history. It's quite a hike from Edinburgh Castle, but it can be done. Might be worth it to take a bus. Not sure how many days you have in Edinburgh, so if you have time, I suggest checking out some of the National Galleries of Scotland - https://www.nationalgalleries.org/
St. Giles Cathedral is nice and also on the Royal Mile. Enjoy!