If you're in Jilikul and interested in visiting museums, you might want to check out the National Museum of Tajikistan in Dushanbe. It's about a 6-hour drive from Jilikul, but it's the largest museum in the country and has exhibits on Tajik history, culture, and art.
If you're looking for museums closer to Jilikul, you could try visiting the Khoja Mashhad Mausoleum in nearby Kulob, which is a shrine to a prominent Islamic figure and also has some historical artifacts on display. Another option is the Kulob Regional Museum, which has exhibits on local history and culture.