Family hotel Edinburgh suggestions?

At least some Premier Inns have a day bed that can be made up to sleep on. It's not a sleep sofa; it has a regular matress--though not a super-cushiony one like they have on their large beds. I've slept on many of those day beds and found them fine. I've found Premier Inns to offer very good value. They have good air conditioning (which is not a given in Scotland, and which you might be glad to have), and I've never had a problem with their Wi-Fi or plumbing.

You will not get local character at a Premier Inn, but I'll happily trade that for a/c in the summertime--though the odds are that it won't be so hot you'd be totally miserable without it.

A key question for your budget is whether you’ll be in Edinburgh during August/festival season, when hotel prices can triple. The Fringe, which is the biggest part of festival season tends to run from the first Thursday/Friday in August for three or four weeks and has an extraordinary impact on hotel room prices. So what you can get in July for $200 and what you can get in August for $200 is very different.

What are your planned dates?

I would consider looking elsewhere for a hotel - maybe one a bit farther from the Royal Mile. I stayed at the Premier Inn on York Place in New Town and loved that area. It was much more residential, quieter and was not packed with tourists like the Royal Mile.

Another hotel there that a few others here have stayed at is the Ibis Hotel on St. Andrew Square (it was actually close to my hotel). Again, a lovely area with lots of restaurants and shops around but none of the Royal Mile congestion.

I agree that you shouldn’t limit your options to hotels on or just off the Royal Mile. Edinburgh is a compact city and very walkable.

The hotel I stayed at in June (Apex Waterloo Place) is just across North Bridge from Old Town, and I could walk to the Royal Mile within a few minutes. That one isn’t within your stated budget, but the aforementioned Premier Inn is, based on a quick look at Booking.com.

Premier Inn family rooms are only available where the children are under 16. Premier Inn Family Rooms so that option will not work for you I'm afraid. However, you might well get two rooms in a Premier Inn for less than $200 if you book early.

We stayed at Edinburgh Holyrood Aparthotel with our 16 year old daughter just a few weeks ago, and really loved the location right off the Royal Mile. 5-10 minute walk up to the more crowded part of the Royal Mile, and less than 5 minutes walk to Holyrood Palace and Arthurs Seat. Small Tesco grocery store one minute walk. We reserved a 2 bedroom/2 bath with a small kitchenette so we could make coffee & quick breakfast in the room.

It cost more than $200/night in June 2023, but for the excellent location, kitchenette, 2 bedrooms & 2 bathrooms, we thought it was worth it. They do have smaller rooms such as studios & 1-bedroom apartments with a sofa bed as well.

My sister and I are booked into the Travelodge on Queen Street - nothing fancy but it fits the budget and is close to everything.
Leaving in 32 days!!

We definitely won't be going in August. Probably early June.