Grand Canyon is a long one day trip - just be prepared to leave early in a.m. & get back late.
One option is renting from your hotel for one day for a car if you don't feel you would need or get the value for it over a 4 or 5 day rental. Then you could still go to Hoover Damn & Red Rock Canyon. With discount codes from the rental car thread (on page 1 of about a 140 page thread LOL) from fatwallet, I did a one day rental at Paris for $48 including taxes last trip. My only change would be to next time rent it the day BEFORE I leave & change return location to the normal rental car center. Might be a few bucks extra for a location change for drop-off but still less than taxi back to airport.
One hotel option if you are not really gamblers might be Desert Rose Resort. They reviews of it have been very good at vegasmessageboard.com. Sounds like they have a continental breakfast also & nice rates. From what I could tell in the reviews it is close to MGM - just walking distance off strip. There is also a Marriott Village type of location east on Flamingo then about a block north (just north of Bahama Breeze I believe) where they have a Springhill Suites as well as a couple other properties. (I'm a big Marriott fan).
Valet parking is free at all strip hotels, however, on weekends it may be restricted to hotel guests or higher level players club members. Self-parking is also free & normally will always have room.
I was VERY surprised at the comment about the casinos being filled with smoke. They are some of the CLEANEST casinos I have ever been in. You will notice differences at the older, lower ceilinged casinos where the air doesn't circulate as well. Example - it is smokier in the front area of Flamingo, the Penny Pit in Harrahs, Casino Royale, etc than it is in Bellagio, Paris, Ballys, MGM, etc. It is the design of the building - older - lower ceilings. But in the bigger ones, I can hang my shirt out at night & it doesn't smell like smoke in the morning. (At our local casino I have to stuff it into bottom of laundry basket because it stinks so bad). I also can breathe easier in the Vegas casinos.
You cannot smoke in any dining areas in Vegas, however, if there is someone bothered by smoke, make sure you are seated away from the exterior areas of the restaurant - example - at Cafe St. Louis in Paris there is an 'outdoor' (it's all inside) patio area - it is adjacent to the casino floor so there could be smoke there from the players. However, inside the restaurant you would be away from it.
Come & visit us at vegasmessageboard - someone here directed me to them a couple of years ago - a great bunch & willing to answer your questions!! Just as friendly & wonderful as the people here.
I have not read too much in the wonderful terms on the West Wing rooms - most people feel you should try to get a Tower room instead.
There are tons of things to do on the strip itself that do not involve gambling - enjoy!