The Tabernacle is a building were lots of meetings are held. It has a big domed roof. Tours of it and many other buildings are offered daily.
One building at Temple Square which tours are not offered of is the Salt Lake City Temple. It is sacred to members of the church, and as such only members in good standing are allowed to enter.
The church did recently make the temple a bit more accessible to those of other faiths. The visitor center on the south side of Temple Square has a scale model which shows the interior of a lot of the building. It's a fascinating display.
The Celestial Room