Market place is in the public area, meaning you can't simply just go there. You need to choose a lot to go to first.
The bar is the closest, so go there. After that, wait until a vendor arrives and puts wares on the table. Click on the items on the table to buy them. There's also a food stall, but if you want sim to enjoy and learn foods from there, raise their culture skill to level 3.
If you click on the vendor sim and choose Buy Explorer Supplies, then you can buy portable toddler bed, plants and books. If you also have Outdoor Retreat, you can find the campfire, tents, portable beds, tables and chairs and guitar. If you also have Cats and Dogs, you also find pet supplies such as pet beds, food bowls, litterboxes and pet toys.
Once your sim maxes out the culture skill (level 5), your sim can also access secret wares. In there, you can find waterfall in the bottle, grilled cheese ready to eat, machete, sugar skull named Art, undiscovered artifacts, relics and refined crystals. There's 3 special foods in the secret menu. Maxing out this skill is definately worth it.