We rent out a flat in central Edinburgh - sleeps 6 and walking distance to everything (New Town) and charge £395 for 3 nights low season. Pm me if you want details or dates. You then save on meals etc. Or try Holiday Inn at the top of Leith Walk although rooms are tiny but cheap.
Castle is good. Arthur's Seat. There was a nice cafe that sold endless combinations of hot chocolate and porridge, that my dds enjoyed a lot - can't remember its name though and no idea if it would still be there!
Travelodge! We've booked 3 nights in a centrally located Travelodge just before Christmas for £30 per room per night. Obviously won't be fancy, but as long as it's clean, we don't need any more than that