Cal filled in a lot of very good points for me. The alcohol law is pretty strange, but most restaurants have gotten around it pretty slick. If you want something more than beer, you just have to know where to go.
That reminds me. Still don’t know if you would have the time, but there is a place called The Mayan that sits around 91st south (as Cal said, the city is laid out in grid with the Temple as the center point so it is south a little ways - 91 city blocks). The food is so-so, but the setting is great. Tropical forest setting that is actually done quite well with cliff divers that do performances off the cliffs and into a pool of water. It’s kinda fun.
My suggestion is to save the trip to the lake for another time when you can pack up a picnic, blankets, swimsuits, and stay for the day. Instead, hop a taxi to Temple Square (probably a 15 or 20 minute ride unless it’s during rush hour).
The LDS Church has expanded Temple Square by purchasing the section of road between the Temple and the Joseph Smith Building and other church office building, including Brigham Young’s home (which is also pretty interesting to tour) and have made it into a very nice park with a reflection pool. You can also enter the Tabernacle where the Choir does their performances. You’ve probably seen the pictures of the huge pipe organ. The new visitor center north of the Temple opened last year. I haven’t been inside but I hear it is very nice.
You’ll also see more than one wedding parties that have just left a temple ceremony with photographers taking pictures of the bride among the gardens.
Be forwarned however, the park as well as the Temple grounds are private property of the church so smoking or drinking is not allowed. As Cal also said, the tour guides do not pressure you to join the Church, they are just there to answer questions and to present their faith. You may be a little taken back by the Mormons and their scrubbed innocence, but all in all they are wonderful people (no, I’m not one :)).
The Jesus planetarium is pretty cool. I think they are trying to give the impression of rising up to heaven to Jesus. Evenso, it’s kinda pretty.
The gardens and fountains in and around Temple Square are awesome as well. I know a gardener who works there and he tells me that the flowers gardens are continuously changed.
If you still have time, walk down to 2nd South and State Street (State Street is the street that runs north and south and begins at the front door of the Capitol Building) to the Galivan Center. It is a park with a sculptures, outdoor cafes, amphitheater, ice skating rink, etc. It is going to be a main meeting spot during the Olympics. Good place for a picnic.
To really see Utah, you should come back for a week or two and visit Zions National Park, Bryce Canyon, Moab, Flaming Gorge, and other spots. For now, I would just stick to Temple Square.