The Rudaki Republican Museum of Regional History sits on the central square of Penjikent, in a Soviet-era pavilion that's seen better decades. The collection is far better than the building suggests: original wall fragments and stuccoes from the Sogdian dig, ceramics from Sarazm, ethnographic displays of Tajik mountain life, a generous Rudaki room with editions of the Shahnameh, and the regulation glass cases of stuffed snow leopards.
The labelling is in Tajik and Russian only; pay the curator a couple of somoni extra and they will give you a guided tour in whatever language works. Admission is around 10 somoni, open daily except Mondays, generally 9 AM to 4 PM with a lunch break.