It's been about 7-8 years since I was in Vegas.
One thing I noticed out there was that many casinos had cheap breakfasts until some very early hour (like 7am). So I'd just get up, throw on some clothes, comb my hair and go to breakfast, then come back to the room and showered and get ready for the day. The restaurants were pretty empty at that hour, so it's not like anyone noticed. LOL And it saved a ton of money.
I loved going out to Red Rock Canyon (about 20 miles west of LV).
Red Rock Canyon Las Vegas Nevada - VEGAS.com
I really enjoyed going to Mount Charleston. It's amazing how much cooler it is than just a few miles south in LV.
Hoover Dam is worth a visit, as is Valley of Fire State Park
Valley of Fire State Park
As you're probably driving right by here, seeing the Grand Canyon from the new overlook on the Hualapai Indian reservation might be worth a stop.
Grand Canyon West | Hualapai Indian Reservation | SkyWalk (On the other hand, your fear of heights may not make this much fun)
I'm not much of a casino person, but really I enjoyed seeing the outdoorsy attractions out there.
As others have mentioned, there's a lot of free stuff to see (the Wildlife Habitat at the Flamingo, the Bellagio fountains, the Lion Habitat at the MGM, the Sirens show at Treasure Island, the car collection at Imperial Palace, the fountain shows at Caesar's Palace, Fremont St. light show, etc. ) More details here
Las Vegas Attractions, Things to do in Las Vegas | VEGAS.com
I did enjoy the Cirque show "O". Most of the other shows out there struck me as pricey.
I did take a helicopter tour after dark. It's fun to see all of the casino lights from the air.
As other have mentioned, driving on the Strip is not advised. There are streets that parallel the Strip that will get you northbound or southbound without all of the hassles.
omni