I spent a month in Peru in 2013 and havn’t been back to Cusco since, so I’m not sure as to how things are now. For the 100-ish range in Cusco, have you looked at Hotel Rumi Punku? It’s a charming little place with great service — they let me early check in right after coming off a night bus from Puerto Maldonado in the morning. I stayed there as well as at the Inkaterra la Casona nearby and from what I remember both were walkable.
Aguas Calientes is small and not really attractive in itself as a base for Machu Picchu. If you want to catch the sunrise, unless you decided to splurge and stay up at the Lodge, you kind of have to stay in Aguas Caliente. I remember Tierra Viva by the river being a decent option. For a nicer place, there’s the Inkaterra Pueblo Inn or the Sumaq.