I'm at uni of Edinburgh now in my second year. I also wanted a a self-catered, en suite singleroom. I ended up in Brae House - and honestly it was good! It's a little run down, BUT the location is actually perfect. It's about 15/20 minutes walk (or 5 minutes bus) to the main shopping area, Princes Street. About a 25/30 minute walk to the uni (George Square campus) which might sound long but I actually really enjoyed my morning walks to uni (and I usually hate walking lol). It's a lovely walk up the Royal Mile, you see Arthurs Seat and some beautiful, typical old Edinburgh buildings - its honestly a really nice walk. You can also get the 35 bus (which is right behind Brae) or the 45 or 5 bus which is from a stop about a 3 minute walk away. Most of the accommodation is the other side of the uni and a little bit nearer to the uni but then much further from Princes Street and I loved being so near to the centre of the New Town and all the shops etc. Also there is a big Sainsburys and a big Lidl like a 5 minute walk from Brae House which you wouldn't get if you lived really near to the uni.
I was in a flat of 9 which I think was on the bigger side - I think the smallest is 4? But we had a MASSIVE kitchen (not the normal size even for 9) but we were just blessed on that I guess. I was in the smaller room but they do offer bigger rooms. I never saw a bigger room but a friend of a friend had one and they are apparently bigger and worth the little extra that you have to pay. But honestly the smaller room is fine, I had enough space and it worked well for the year tbh.
I loved the area so much I chose to stay in the same area this year just in private accommodation. It's near Princes Street and the shops, but also near Leith Walk and Easter Road both of which have some lovely independent shops and cafes. It's also SO near Calton Hill which my friends and I go up every evening when its sunny. It's also near Arthur's Seat and Holyrood Park which are also lovely. It's so well connected with bus routes, literally there are buses nearby that will take you anywhere in Edinburgh. You're also on the side of the town nearer to the beach which is fun. Honestly people like to live in the area where the majority of the accommodation is but the Brae House area (Abbeyhill, Easter Road, Meadowbank) is SO nice, I felt really safe and I was never bored. There really are so many benefits to living in this part of Edinburgh as opposed to south of the uni. My friend is living in Marchmont this year and she's moving next year because she's so bored of Marchmont.
Also, someone mentioned kincaids - it is known to be good for social and it is central but it's loud, it's on Cowgate (the clubbing street) so if that's what you're into then you'll probably enjoy, but it wouldn't have been my kind of thing. Also I've heard it has rats so...