Having taken my kids, aged 8 + 11, last year in October, I can tell you what worked for us. YMMV.
- We walked up to the castle, but thought the price was too much for what was on offer for the Children. (and I'm not sure we would have bothered as adults only)
- The Camera Obscura was fun and the whole exhibition enjoyed by the children
- 8 year old pretty scared at the Dungeon - not a bad way to spend some time. Maybe too corny for some.
- Real Mary Kings Close was worth paying for. Interesting tour.
- National Museum is a *must*. They have free tours of some of the collection by Volunteer Guides. We joined a Viking one and it was excellent - brough the exhibits to life
- Walking through the streets - Royal Mile et al. Free and fun.
- Toy museum. OK if it's raining or if you have 20 minutes to spend in nostalgia.
Mary Kings close and the Dungeon both allow online booking, which gets you a cheaper rate and the chance to dodge the queues. The close does book up, so book before you arrive if it's something you fancy doing.
Also very surprised that all the low-end restaurants were booked and we couldn't walk in off the street on a wet night in October - it was English, not Scottish, half term and the place did not seem overrun. Moral - make some reservations if you want to be sure of eating somewhere you fancy.