January is one of the rainiest times of year to visit Machu Picchu (after February, the height of rainy season, and tied for second-wettest with March)—but it is also one of the warmest months in the Peruvian highlands, with highs around 66°F (19°C) and lows around 45°F (7°C). This makes it one of the months with the least temperature variation.
Bear in mind that the Inca Trail and Machu Picchu this month may well be less crowded, mainly because of the weather, but that the rain brings some big risks with it. Landslides can affect the trail, which is at its most eroded after almost a year of being tramped since last season's maintenance. Landslides can also affect trains between Cusco and Machu Picchu (Aguas Calientes railway station) and flights between Lima and Cusco. Even if there are no landslides, the going is still excessively muddy, possibly the muddiest of any month for hiking.
The general wet season pattern is that the bad weather comes in the afternoon, so get a morning flight to avoid cancellations.
Crowds & Costs
After the Christmas and New Year surge in tourists, and before the February closure of the Inca Trail, the Sacred Valley is full of surprisingly good deals on hotels, and even adventure tour agencies can offer special deals on activities. Tourism on the Inca Trail and at Machu Picchu is still significant compared to most places in Peru, but far quieter than at most other times of the year. If you have previously visited the Sacred Valley at a different time of year, you will notice the reduced crowds in even the most popular areas.
Importantly, this is also the month when Inca Trail permits go on sale, with January one of the key months to book the Inca Trail for a later month of the year. Popular months do sell out fast, and several months in advance.
Where to Go
The wet weather may incline you to spend more time exploring the towns in the Sacred Valley with more to do indoors. Cusco is the obvious starting point here, although Ollantaytambo and Pisac are also pretty towns with great cafes, restaurants, and hotels in which to relax however wet it gets outside.
What to Do
Machu Picchu is not just about the ruins themselves (perfectly fine to visit this month) or the Inca Trail (okay to trek this month, although it is not the best month to do so). There are many other activities to do in the area that are not weather dependent, such as the museums and superb dining scene awaiting in Cusco. See here for more on how to spend 24 hours in Cusco.
High water levels make for better, faster rafting, and January is one of the best months for rafting in and around the Sacred Valley: rains swell several rivers into Class IV rapids. And higher water also brings you closer to the jungle canopy, meaning sightings of canopy animals and birds might be better when you are out on the river.
The wet January weather is also great for botanists and plant-lovers: flora is first-class at the moment on the Inca Trail, and adds a spray of color along the way.
Bear in mind that if you wish to travel by train between Cusco and Machu Picchu (Aguas Calientes train station) this month, services from Cusco's Poroy train station are not operating: you will be taken by bus from for the Cusco-Ollantaytambo leg and continue by train to Aguas Calientes from there.
Cusco has plenty going on throughout the year, even in January. January 1 is very much a case of the morning after the night before, when the celebrations for Año Nuevo (New Year) for which Cusco is famous take place. The month's best celebrations happen a little later on.
Bajada de los Reyes Magos: Lying between Cusco and Machu Picchu, and a transport link between the two, Ollantaytambo celebrates epiphany between January 5 and January 8 with this festival translating as the 'Descent of the Three Wise Men'. Dances and other celebrations culminate, as is common throughout the tradition-steeped Andes, in a bullfight.
The festival is the official wind-down from Christmas celebrations, and is also celebrated in Cusco, but Ollantaytambo has the most colorful festivities. Ollantaytambo also has one of the most important and most used train stations in Peru: see here for more on Peru's best train rides, including the journey between Cusco, Ollantaytambo and Machu Picchu.