OP, taxis back and forth may be doable but it is a fairly long trip and I'm not sure "ANY" taxi you hail on the streets will take you. May need to make arrangements before hand. When I was there, it seemed most were local only. Don't get me wrong, I like the Tambo too. It is a great place ... just not the convenient for visiting Cusco. For the sacred valley sites, its great. You can consider getting a driver to take you to 2 or 3 sites (salt mines, etc) in a day. I found a pretty good contact here on FT in an older post. If you want it, I can go dig it up.
For Lake Titicaca, I highly recommend Isla Suasi. It is on a private island on the east side of the lake. Not many places come close. It is consistently rated on Trip Advisor as the top hotel in the area. If you choose not to stay on an island, then there are a whole bunch of hotels in Puno.