Morning: Go early to Batu Caves. From KL Sentral, KTM is the easiest DIY route, or use the Private Half-Day Batu Caves & Cultural Temple Tour with Transfers if you want less friction. Be there close to 7:30am. The steps feel much longer after 10am, and the monkeys get bolder once crowds thicken. January is a good compromise: there is real pre-Thaipusam movement around the temple, but not February-level pressure.
Breakfast: If you're starting from KL Sentral or Brickfields, stop for roti canai on Jalan Tun Sambanthan. Eat fast, drink teh tarik, and move on before the heat builds.
Midday: Back in town, spend time in Chinatown. Walk Sri Mahamariamman Temple, Petaling Street, and Chan See Shu Yuen Temple at a slow pace. This part of the city makes more sense in January because festive stock starts appearing without the heavy Chinese New Year crowd wall.
Lunch: Go to Kim Lian Kee around Petaling Street for KL-style Hokkien mee or chicken rice. You can walk there directly from the market lanes.
Afternoon: Cross to Central Market and nearby heritage streets, or keep things cooler with a short museum stop. January showers often show up around now, so this is the right window for covered arcades and indoor browsing.
Evening: Head to Kampung Baru for satay or grilled fish. The old Malay neighborhood feels especially good after dark, when the towers rise behind low-slung streets and smoke from the grills hangs in the air.