I would definitely rent a car, because some of the best adventures with kids will be outside of town. We were down there with my 9 and 12 y.o. in December, and their favorite thing that we did was the Hoover Dam. You'll need a car for that.
We also went to a Cirque du Soleil show (yes, it's expensive, but so much fun). The aquarium at the Mandalay Bay was also surprisingly good - I did not expect a casino to have an AZA accredited aquarium.
Some of the casinos have exhibit space. Check AAA and other travel websites to see whether there is anything worth seeing. While we were there the Venetian hosted an exhibit of the 50 best photos from National Geographic, and it was spectacular. Another casino was hosting an Andy Warhol exhibit that we didn't get to, but probably would have enjoyed.
While we didn't get there, I've heard wonderful things about Red Rock Canyon, and Valley of Fire State Park is less than an hour's drive from town, and supposed to be stunning. Just remember that you are in the desert. Everybody should have a water bottle, and sunscreen and hats are essential. If you're doing any hiking, wear closed toe shoes. There are some unfriendly plants and small critters in the desert.
My mother and her husband, who were there with us, chose not to rent a car because they had been told by friends that they could get around fine with public transportation. However, the friends that told them this had stayed on the strip, and we did not. My kids and I left 3 days before they did, and without me and my car they had a terrible time getting around. While there is good public transportation to main attractions around the strip, getting back to lodgings was a different story - multiple connections and long waits. And since they also arrived before us, they had to pay for a shuttle to and from the airport. According to my mom, it cost them $35 to get the 8 miles from the airport to our lodgings. A rental car would have ultimately cost them little more than they spent on transport. Traffic in Vegas can be heavy, but the parking situation was surprisingly good. Many casinos have spacious parking garages, and many are free. (They do want to make it easy for you to come and spend money, after all.)
As for folks handing out dubious advertising and such, we saw them but were never approached, probably because we had children with us. There are ads on taxis and buses and signs for some of the more "interesting" shows, but the ones I saw were PG.
To reach food and shows on the strip, you usually have to walk through the casino spaces. The cigarette smoke can be thick, and your kids might see things that require discussion later. (Mom, why are those women wearing that? What are those machines? And so on...)
If the Stratosphere has good swimming pools, that may very well be your kids' favorite part of the trip. In May the weather should be perfect for swimming. Take sunscreen and enjoy.