Upvote:1
Ollantaytambo is better suited for hikes than Cusco. But, you can easily go for hikes around Cusco as well. The possibilities from Aguas Callientes are limited. (And, it's not a very nice town if you're not going to Machu Picchu.)
In Cusco, everyone and their brother will be able and willing to get you on day tours. But, I would probably start by asking the guys from the Cusco Free Walking Tour. I'm not affiliated, but, their city tour is quite good (though their tour in Arequipa is, well, awesome) and I'd say they genuinely will try to help you in finding good day trips, or point you to the people that can.