If you got some energy in you, there's a few great hikes involving a bit of legwork. Do make sure that you've taken the time to acclimatize to the elevation either in Cuzco or Aguas Calientes for a couple days before exterting yourself too much, especially on Wayna Picchu.
Wayna Picchu: Towering above the north end Machu Picchu is this steep mountain, often the backdrop to many photos of the ruins. It looks a bit daunting from below, but while steep, it's not an unusually difficult ascent, and most reasonably fit persons shouldn't have a problem. Stone steps are laid along most of the path, and in the steeper sections steel cables provide a supporting handrail. That said, expect to be out of breath, and take care in the steeper portions, especially when wet, as it can become dangerous quickly. There's a tiny cave near the top that must be passed through, and is quite low and tight of a squeeze. Take care at the peak, it can be somewhat precarious, and those afraid of heights may want to hang out just below.
The entire walk: is through beautiful landscape, and the views from the top are stunning, including birds eye views over the whole site. There's also a few ruins near the top. If visiting these ruins, you'll see a second way to start making your descent down the mountain, along some very steep and shallow steps.... these steps are a bit dangerous if wet, but the hike may be well worthwhile. This hike is one of your best bets for getting away from Machu Picchu and Wayna Picchu crowds.
Access to Wayna Picchu: is limited to 400 visitors per day. You must sign in at the entrance gate, and take note of your number, as you're required to sign out upon your return. The first 200 numbers are released at 7:00am, and are often gone in less than an hour on busier days. The second 200 are available at 10:00am. All visitors must arrive back at the checkpoint before 4:00pm. Get here early if you're intent on climbing it, and note that large tour groups are able to reserve numbers and jump the queue, so don't be miffed when you're in line and a guide saunters past with 20 people in tow.
If you have some time at hand, or long for a sparkle of solitude, you can also walk to the Moon Temple (Templo de la Luna) and the Great Cave (Gran Caverne). It's a long walk and adventurous hike involving several ladders. Some may find that the sites aren't really rewarding, but unexpected wildlife can be seen (wild spectacled bears have been reported). This hike is also quite interesting because partway through you leave behind the mountain terrain and enter a more conventional forest. The caves can be reached either by hiking down the trail from the peak of Waynapicchu (which includes some semi-harrowing but fun near-vertical descents) or by the split from the main Waynapicchu trail (look for the sign that says Gran Carvern). Remember that it is much easier to descend from Waynapicchu than to ascend from these temples. Be sure to bring plenty of water and snacks for this long hike. The hike from the summit to the caves and back to the checkpoint takes about two more hours.