As someone who lives there.... I'd rather shit in my hands and clap than leave the house right now 😂 it's awful. So, so many people (ignorant twats who can see you coming with a double buggy containing a 15 month old and 7 week old but still take up the entire breath of the street), it's my literal nightmare right now. Theres loooooads to see and do, and the fringe has some amazing performers, but its very too crowded for me, as I said I took mine out earlier, came home after 20 mins cause I was seriously in danger of losing it and either screaming or throat punching someone for barging into me or the buggy. BUT that's just me, I'm cranky af lately thanks to having a 15 month old and a 7 week old 🙃
Your kids are a bit older so might not be such an issue with the busy peopley part, just make sure they know to stay by you and put your phone number on a bit of paper in their pockets, just incase - it really is super crowded around the fringe bits so better safe than sorry!
Arthur's seat is always awesome, I've walked round it hundreds of times (once tipsy, that was nor a good idea and swiftly turned round again when it became apparent we were being very flopping stupid) but never fails to amaze me. Another good shout (and a free one!) Is the museum on chambers Street. It's massive (literally can't do it all in a full day) with loads of really cool exhibitions the kids might enjoy depending on their interests. Could be a good shout if it's raining, which ... well it rains here all the time lol.
Dynamic Earth is also cool af, really informative, interactive and educational,(but kinda pricey) that's at the bottom of Arthur's seat so close to go for a wee wander.
The Edinburgh dungeons are also fricken cool, I took my 12 and 8 year old niece and nephew there 3 years ago, they still rant about it 4 years later. Interesting wee tour rhag has actors on it to tell yoh about Edinburghs history with the plague etc.
Bring a rain coat, dress in layers cause it goes from rain to boiling in about 0.23 seconds over the last few weeks, but mostly importantly- have a fab day making memories with your wee ones! The train journey up is also pretty nice from your area, lots of scenic views.