Hoover Dam still ranks as one of the nation's finest engineering achievements. It is only 30 miles from Las Vegas, and the views of it are free, although parking is $7 USD. If you do make the drive, taking the power plant tour is worthwhile, but it is $11 for adults. You can make advance purchases for tickets. A longer, more detailed tour is available for $30.
Lake Mead Recreational Area offers sport fishing, kayaking, canoeing, hiking, picnic areas and some of the most striking desert scenery you'll see anywhere. The contrast between the lake and the barren landscape surrounding it makes for great photographs.
Another photographer's mecca not far from Las Vegas is Red Rock Canyon National Conservation Area. Take Charleston Blvd. or Summerlin Parkway west and you'll run into this picturesque place, close enough (15 miles each way) for a comfortable day trip from Vegas and yet worlds away from the bustle of The Strip. Hiking and picnic opportunities abound.
In Las Vegas, you'll see a lot of advertising for various Grand Canyon tours. Shop carefully, as some of these excursions are overpriced. Recognize that driving to the Grand Canyon and back in one day from Las Vegas involves covering nearly 600 miles, and that will leave very little time for admiring the wonders of the canyon. It's best to spend the night at the canyon or perhaps save that visit for another trip.
One possible alternative is a trip to Zion National Park, about three hours from Las Vegas in southwestern Utah. The views here are astounding and there is a free shuttle bus that takes you through the park to the lodge and various hiking trails. It costs $25 USD for a vehicle to enter Zion (good for seven days), but when you look at the ticket price for one Vegas show or admission to a theme park, $25 is rather modest.
Consider buying a Las Vegas Explorer Pass. This is a card you buy prior to your trip and then activate on first use. You can choose from a Grand Canyon Tour plus two "wild card" choices from a list of 22 attractions, shows and tours ($149) or an Ultimate Variety Show pass good for that show plus two wild card options ($109). Make your Vegas plans before you consider a Las Vegas Explorer Pass purchase, to determine if the investment will save you money on admissions.
There is also Death Valley National Park in nearby California. Entry fees are $20 for a one-week vehicle pass or $10 for an individual visitor.