Temple Square is the historic and religious heart of Salt Lake City. It's here that you find the Mormon Temple and Tabernacle (and if you're lucky will have a chance to hear the Mormon Tabernacle choir as it rehearses).
You'll also find extensive gardens including 250 flower beds and over 165,000 plants from all around the world. The gardens are redesigned every six months by a staff of full-time gardeners and volunteers. Plants are grown off-site in greenhouses owned by the church.
Anyone can visit Temple Square, and I encourage you to do so. The worst thing that can happen is that a polite young missionary will ask you if you're interested in learning more about the Mormon faith. You can always say "no" and they will leave you enjoy your visit.
The colors and playfulness of the gardens make them most enjoyable!