Harrah's is in a good location as it is fairly central. I have read that the rooms are quite small, but that may be by Vegas standards so I'm sure you will be happy with them if you are used to the rooms in say Spanish resorts. There is also a monorail stop at the back of the hotel which will get you to the MGM in about 5 mins for $5. Walking would take about 45 mins to an hour.
You can't do the GC South Rim by helicopter as it's too far. We did it in a Cessna, but I can't recommend it as the turbulence was horrendous and spoiled the experience. I think there are trips that fly you to the canyon then you get on a helicopter.
Re shows, once you have an idea of which ones you might like to see, post them here and someone will be able to suggest the cheapest way of getting tickets. I can recommend the Jersey Boys at the Palazzo which is excellent, however it will be a lot more expensive than seeing it in say London. Terry Fator is also an excellent show. He is a ventriloquist who won America's Got Talent. I enjoyed it far more than I expected to and have seen it twice. There are several Cirque du Soleil shows. The Love one is based on the Beatles music and is very good. A great free show is Big Elvis at Bill's Gambling Hall. I think he is on from 3-5pm, but you need to get there early to get a seat. He doesn't look like Elvis, but he certainly sounds like him.
Tix4Tonight also have something called Tix4Dinner where you can get up to 50% off entrees for a $3 per person fee.
In addition to the shopping mentioned, there are also the Premium Outlets near downtown
http://www.premiumoutlets.com/outlets/outlet.asp?id=58 You can get there on the Gold Line bus which is much faster than the Deuce as it is an express service. Stops going there are at the MGM, Paris and Wynn. Coming back the stops are the Fashion Show Mall, Bellagio and Excalibur. The fare is $7 for a 24 hour pass.
luci