Just got back from a week in Peru. The Hilton Garden Inn in Cusco is very nice and about a 10-15 walk from the city center. They have a free shuttle in the morning and at 9pm. The area between the hotel and downtown is safe and quiet, but be warned that the hotel is uphill. It is actually a great primer for MP. The taxi from the airport is around $6-7, while the taxi from the hotel to Ollantaytambo is 100 Soles. I recommend the 7 AM Huayna Picchu ticket to avoid the heat. There will be plenty of daylight at 7AM. (BTW, it is called Huayna Picchu on the ticket, but Wayna Picchu on the signs inside the park, one of the many truly screwed up things that you will encounter when traveling btw Cusco and MP).
I feel like one day and one evening in Cusco is adequate. I found Ollantaytambo to be much more charming, but it is very small. Aquas Caliente is a truly horrid place, and the lodging leaves much to be desired, much like the companies that run the rail service and M.P. They get away with being horrid because they have a monopoly on Machu Picchu and they know it. Personally, I had zero issues with altitude sickness (I live a few blocks from the ocean). Coca tea is quite abundant (freely offered in many hotel lobbies), and there are other coca candies you can buy. I did get exhausted while climbing up Wayna Picchu, but I had a backpack with all of my stuff and despite not being overweight, I'm not really in great shape. I had no problem going downhill or walking across a level surface.
I actually really enjoyed Lima more than I expected. I walked all over the historical city center during the day, and I walked over pretty much all of Miraflores, San Ysidro, and Barranco during the day and night. I recommend staying in Barranco or Miraflores. There is a BTS bus that offers a convenient but crowded option for traveling around Lima. It has dedicated traffic lanes, so it is quicker than a taxi and only 2.50 Soles per trip. I would not bring any valuables or baggage on board, but it is great for getting downtown and back as long as you do not mind a bit of a squeeze. I was actually quite surprised at how large the affluent part of town is (pretty much everything including and between San Ysidro and Barranco). There is a very stark contrast in wealth in the city, and I felt truly poor while walking around much of it. Also, be sure to check out Huaca Pucllana in Lima (Miraflores). They have day and night tours. The night tour does not go to the top, but the beauty of the contours and shadows in the light made it more enjoyable for me.