Solo traveling--Santo Domongo to Lima to Cuzco to Machu Picchu?

You should have no problem. Fly from Lima to Cuzco (you can also take a bus, but that takes really long ,-about a full day). From Cuzco you have to take the train to Machu Picchu ( no roads go all the way to Machu Picchu. You can go by bus to Ollantaytambo (about half way to Machu Picchu), but then you ran the chance of not getting a seat on the train from Ollantaytambo to Machu Picchu (the train fills up in Cuzco)). To go to Machu Picchu, the fastest no thrills trip, should take 3 days. One to fly to Cuzco (the train to Machu Picchu leaves early, so that day you should visit Cuzco, the Coricancha temple, Sacsayhuaman, etc). The next day leave early to Machu Picchu and return at night and the next day you can fly back to Lima (actually it would be 2 1/2 days). I'm enclosing the web page for the train to Machu Picchu. Bear in mind there is only one company operating the route to Machu Picchu, so that will probably be your bottleneck.