The closest town to Machu Picchu is Aguas Calientes, soon to be renamed Machu Picchu Town. The town is named after the hot springs located 10 minutes away. For a small fee, you can soak in the hot springs, though it can be rather nasty when there are dozens of tourists there, some even bathing themselves. The town is mainly a pit stop for people going to Machu Picchu. Most tourists just briefly pass through when they go to/from the ruins. Some come a day before they visit Machu Picchu and stay in one of the expensive hotels in town for the night. Others, like me, rest here for a day after hiking the Inca Trail, before heading back to Cusco.
The railroad runs straight through the main drag of the town. When arriving from Cusco, the train drops passengers off directly in front of shops and souvenir vendors, so be prepared to be hassled by locals to buy Kodak film or a T-shirt that says "Machu Picchu" on it. After the train station, the tracks continue through town, where they are lined by dozens of restaurants and Internet cafés.
Just north of the main drag and railroad tracks is a rather large market. Like any market in a tourist spot in Peru, you'll find the same things you can find in Cusco, Pisaq, or any place in between. However, expect to pay more here. Everything in Aguas Calientes is more expensive than elsewhere. At the train station, I found a snickers bar for almost $2.
From the main square, Plaza de Armas, you can also find lots of small tourist shops and restaurants. The prices at any of these places are very close to American prices, so don't expect to find anything cheap like in Cusco.
If markets are not your thing, try hiking up Puticusi Mountain. Walk along the railroad tracks towards Machu Picchu, away from town, and within 5 minutes you'll come across an entrance to the trail. On my visit, I had so badly wanted to hike this, but it was raining. My guide from the Inca Trail said not to hike it in the rain, because there are wooden ladders that become very slick when wet. So hike it at your own risk. If you do hike it, I hear you will get spectacular views of Machu Picchu.
Overall, Aguas Calientes is a colorful and unique town. Unless you plan to spend 2 days at Machu Picchu, staying here for more than a day is not necessary. There is only so much of the markets and 14.4kbps modems at the Internet cafés you can handle.