We have visited the interiors of seven state capitols now, and Mississippi's is the most beautiful, detailed one we have seen (shhh, don't tell anyone in Texas). It's small, so it can be thoroughly toured in an hour (and in 30 minutes if you're in a crunch),
They have set tour times; however, there weren't many visitors when we were there, so we got a free, private tour from an extremely knowledgeable volunteer tour guide.
Generally, you can visit the House and Senate chambers, the original Supreme Court chamber, and of course, the rotunda.
Old State Capitol
This was closed for renovations, so we just took a look at the outside. The pictures look beautiful, so stop by once it reopens!
Mississippi Art Museum
This is a free museum. Our favorite parts were the Peruvian pottery, the photography exhibits, and the quilts. Expect more Mississippi-related art and less "big name" artists than you might see at other art museums.
This outdoor memorial is next door the Old State capitol so walk over and take a look.
Civil Rights Museum & Mississippi History Museum
These museums are connected together and one admission ticket grants you access to both. We just visited the Civil Rights Museum. If you do want to visit both, you might try to visit one museum in the morning, break for lunch and come back to visit the other. The Civil Rights Museum is huge. It's practically impossible to read every informational panel, so you'll have to pace yourself. It's incredibly thorough, and we learned a ton. Some of the content may be disturbing to children, but they marked those exhibits well
This an authentic 50's diner featuring breakfast, lunch, shakes, malts, and ice cream. Most notably, a scene in The Help was shot here. The food was yummy but portions are small and service isn't of particular note. However, still worth a stop (for a malt if nothing else).
Cultivation Food Hall: This is an indoor food hall featuring several different boutique food establishments. It's a neat place to visit and works great if people in your group are craving different types of food. There's also a nice outdoor green.
Pig and Pint: Enjoy some pulled pork nachos on their (heated-in-winter) patio.
Farmers' Market: On Saturdays, they have a large farmers' market at the fairgrounds that includes produce, meat, honey, and handcrafts. Eat an apple turnover for us!