For religious reasons, I don't
- drink alcohol
- engage in fornication
- visit prostitution or strip clubs
Are there still interesting things for people like me in Vegas?
It is a week-long business trip, with a weekend stay.
Las Vegas has a wonderful (and inexpensive) sinless side. The costs of running it are subsidized by the gambling industry. You can
wander around looking at beautiful buildings and imitations of the Eiffel Tower, pieces of Venice, a circular escalator, amazing fountains, a fake volcano with nighttime "eruptions", and so on. All free
visit wildlife from flamingos (free) to sharks, dolphins, and tigers (not free.)
You may be irritated by the amount of money that has been spent for no purpose that could have fed, vaccinated, or educated children the world over. You may be offended by the behaviour of people who are busy sinning as much as they can. I especially disliked (after dark, on the strip itself) the people wearing Tshirts advertising how quickly "girls" can be "sent to your room" and the driving billboards featuring nearly naked women in lascivious poses. Many of the street-level touts were engaging passersby trying to sell them things. They focused mainly on men who were alone. My daughter and I were invisible to them. We just walked from place to place as quickly as we needed to and ignored the subculture of the streetcorner, or observed it anthropologically.
If you can abide the ambience on the strip, there is plenty for you to do that isn't sinful at all. Check the las-vegas tag here for more details. I have been on three business trips, and a leisure trip with my twenty-something daughter (a chef) and while we did have wine with dinner we did nothing else that is on your list of things not to do.
Here's a list of shows in Vegas. Since it has "adult shows" as a separate category, most of the others should be OK for you.
I can personally recommend Cirque du Soleil - While some of the costumes can be skimpy, I don't think it would be considered objectionable on religious grounds except by the most ardent fundamentalists.
The Blue Man Group should be completely safe.
The town has been founded by the church of Jesus-Christ of latter day saints. You can visit their temples there. They'll certainly tell you how not to sin in Sin City.
The Penn & Teller magic show is awesome, as are many other shows. Penn & Teller is generally free of gratuitous flesh and they have a strong libertarian philosophical bent they weave into the show.
Vegas also has a number of places where you can go and rent really large guns, like fully automatic things and even I think grenade launchers, and shoot them at things.
And speaking of large things there are also places where you can rent and play around with heavy earth-moving machinery like bulldozers and dump-trucks and scoops.
If you like nature, Red Rock Canyon is fairly nearby (need a car), Hoover Dam is pretty cool and you can rent helicopter trips over the grand canyon. Or you can also visit Valley Of Fire state park which has some spectacular colors and rock formations, about 1/2 hour away from Vegas to the east along I-90.
There are also historical options, like the graveyard for neon signs, or gold mine tours. And don't forget the value of simply wandering up and down the strip, visiting hotels and admiring the opulence.
And don't forget one other option - eating! Vegas has many fantastic places to eat. The casino buffets are full of plentiful but mediocre (ranging to horrible) food but if you don't mind spending a lot more for a meal you can get an amazing meal at many top-end restaurants, or even very good food at a number of moderately priced places.
Not a problem!
For the sheer visual spectacle,a walk down the strip from end to end is an amazing experience. Many of the themed hotels have shows of sorts outside - Treasure Island has a pirate battle every hour, Mirage has an erupting volcano, and the dancing fountains at the Bellagio are world famous!
Each of the big hotels has amazing dining and shopping - just wandering around the dining 'street' inside Paris, or the amazing mall at Caesar's Palace is incredible.
then there are the shows. Blue Man Group, Cirque de Soleis and many more are non-adult themed and very very good. Check what's on the nights you will be there.
Depending on your hotel, you may also have a pool, something I didn't appreciate until last time I was there - a few hours in the morning just relaxing in the Vegas heat was fantastic :)
There are also some amazing themed(?) stores - M&M world, for a start, if you've got a sweet tooth.
Also head up to the old area of Vegas on Fremont Street to see the older Vegas strip of sorts.
If you're prepared to hire a car, there are numerous spots near Vegas - Hoover Dam is an hour away and really worth a look, and there are a few canyons (eg Red Rock Canyon) and the like that are very doable for a day's drive. You could even get a helicopter ride / plane ride over the Grand Canyon!
Enjoy it - you don't need to sin to have fun :)
The Hoover Dam is nearby, there's also fairly expensive helicopter rides over the city.
To avoid sin altogether, avoid the Strip altogether. Believe it or not, you can even get a hotel room off the Strip.
Red Rock Canyon, as others have mentioned, offers beautiful hiking.
The Hoover Dam, also mentioned previously, is within driving distance.
In addition, you can combine a Hoover Dam trip with a Grand Canyon trip. I don't work for this company and can't vouch for them, but the link provides an example of what is available.
You can take day trips to amazing natural sights in the surroundings. Although not technically in Las Vegas, they can very well be carried out with Las Vegas as a base. For me, the first part of the USA I ever saw was Las Vegas, and I thought it was, well, ugly (to be fair, I didn't see very much of it). Having never seen a desert, just renting a car and leaving the city was an experience in itself. Some spectacular places to visit:
all within a day's drive of Las Vegas.