Edinburgh is an amazing place to visit at any age. For teens, you could book a ghost tour? There are several in the gothic Old Town, both walking tours and Ghost Bus/Horror tours - just Google to see what gets the best reviews. Similarly, there is The Real Mary King's Close tour, about a street walled up when everyone contracted the plague.
JK Rowling wrote her early Harry Potter stuff whilst living in Edinburgh and there are also Harry Potter tours.
If you like being by the sea, you could visit Portobello? It's about 10 or 15 mins on the bus from the city centre and has a sandy beach and promenade with lots of nice places for chips or snacks. There is also a fab bookshop in Portobello High Street with really good sections on everything including Young Adult.
A museum your teens might enjoy is Our Dynamic Earth as it's interactive and all about the environment and the natural world eg volcanoes, earthquakes.
Theres also a Chocolatarium in central Edinburgh which does tours, which I haven't been to but which is meant to be nice.
The Scottish Parliament also does tours, which I haven't been to for a long time but which I remember being really interesting. The space is so different from the Houses of Parliament in London. Even the debating chamber is a different shape...a horseshoe so they are not facing each other like adversaries, unlike the House of Commons. Our Dynamic Earth is basically next door to the parliament.
If you want to climb somewhere to get great views of the city you can climb Arthur's Seat, or for a bit of an easier climb that's closer to the centre, go up Calton Hill.
I don't know about hotels but Premier Inns are usually pretty reliable. I know the city well as I was a student there so if you are thinking of certain areas I can say something about them if that helps.