Holiday Inn Leith - Waterside
A hotel we're recommending is the Holiday Inn Leith Waterside. It's nothing special, however, with it being slightly outside the city centre is significantly better value than many other Edinburgh hotels. That said, there is a tram stop just along the road from it, (just 2 stops away from our place), meaning it's dead easy to get to from airport or station. And it's near to us for Saturday activities.
Check out the hotel information page here: https://www.ihg.com/holidayinnexpress/hotels/gb/en/edinburgh/edblh/hoteldetail/
If you are going to book, I have a link which gets you access to IHG's Friends and Family Rate - often the lowest, non-refundable rates are the unchanged, however, often the Friends and Family rate gives a significant reduction on stays with free cancellation.
To book using the Friends & Family discount - use the following link: http://www.ihg.com/h/d/6c/1/en/friendsandfamily?key=WheNoNkzK9YuYimvSnY53M9EW2wJi3pCYQL1GH25JeM%253D&cm_mmc=DCE-_-FF-_-20090228-_-EM12333