If museums are on your list of things to see in Shilda, then you might want to head to Nekresi Monastery. If you want to experience more of the culture Shilda has to offer, head to Ilia Lake and Shaloshvili Cellar.
Pirosmani Museum is 0.7 mi (1.2 km) from central Sighnaghi, why not stop by during your stay. If you want to experience more of the culture Sighnaghi has to offer, head to St. George Church, Bodbe Monastery, and Lost Ridge Horse Ranch.