I've only been to Vegas once, in 2009, but I'm heading back in 2019.

I'll be there in April and I had a doozie of a time finding a hotel for under $100 a night ANYWHERE in Vegas (after you factor in the exorbitant resort fees). I ended up with a place pretty far from the strip that seems pretty nice, called the Eastside Cannery. It has decent review scores on all the booking sites and looks pretty nice from Google Street View.

In 2009 I made the mistake of considering Grand Canyon Village to be a day trip from Vegas. It's a 4-hour drive each way, which severely limits your time there, and unless you don't want to get back to your hotel in Vegas until after midnight, you won't be able to stay for the sunset, which is the best part of a Grand Canyon visit. So I'd recommend reconsidering GC as a day trip. It's better as at least an overnighter.

Near Vegas, however, there are three places which are not to be missed for desert scenery and day hiking:
1) Red Rock Canyon National Conservation Area - 20 minute drive west of Vegas, spectacular place. Go during mid-week to avoid the worst of the local crowds
2) Hoover Dam - 20-30 minutes east of Vegas, also spectacular. Take the dam tour, but also walk across the dam, and consider walking across the bypass bridge downstream of the dam
3) Valley of Fire State Park - about 75 minute drive northeast of Vegas, full of great hikes both short and long, and scenery no less spectacular than the surface of Mars. Allocate a whole day for VoF.

Note: All three of these destinations will be hot, hot, hot in May, so be sure to take all of the standard dessert safety protocols (drink lots of water, wear wide-brim hats to protect ears and necks, wear loose, baggy, long pants and shirts to protect arms, etc.)