Hello,
We are going to Las Vegas for four days, and we want to spend one day touring Grand Canyon. From reading the other posts, it seems that the basic choices are either West Rim, not recommended, or South Rim, ten hours driving for the day. Does anyone know of any fast ways to get to South Rim? How come the heli rides only go to West Rim? If not, should we opt for Bryce Park day tour instead of West Rim heli ride? Any suggestions are greatly appreciated.

Best will be if you stay over 1 night in or near the park. It is a longdrive and you need time for stops.
More or less the same if going to Bryce, possible if you would go to Zion.
Helirides indeed only from the Southrim, probably a regulations to limit noise in other areas.
Maybe you can opt for a small plane daytour to/from Las Vegas to avoid the long drive.

Your post doesn't say when you are going. Bryce weather can be iffy in the winter. Zion can be iffy, but probably will be ok. I think you would be happier to stay 2 days and stay 1 night on the canyon rim if possible. If you are going in the summer, keep in mind that GC and Zion can get very warm.

Two other possibilities to consider:

There are scheduled flights between Las Vegas and Grand Canyon airport in Tusayan. From there you can get to the Rim via taxi. This is NOT a cheap option.

Take a bus tour from Vegas and South Rim. You'll leave early and arrive back late, but at least you won't have to do any driving.

I've never done either of these, so I can't recommend any companies. But you can, at least, check these out.

I have done several things: Driving to the north rim, driving to the south rim, staying overnight, the flight to west rim.

Do not drive to and from in one day. It will be a torture and the drive is anything but scenic. A bus tour will take 16 hours!

My recommendation if you have only 1 day for the Canyon:

Take a flight from Las Vegas. There are many options (depending on your budget).

We took the cheapest flight to west rim without landing (105$) and, I can tell, it was very good. South rim air&bus is better, but more expensive (230$). West rim + landing has not been recommended here on this forum.

Of course, it is special if you stand on south rim during sunset or sunrise (we have done both), but the flight is still recommendable.

And it is a quick&easy option if you do not have much time. We booked this agency:

http://www.looktours.com/Airtours.html

There are others, too.

We've have done the trip from Vegas to the GC twice. Once to the North Rim, Bryce and Zion, once to the South Rim. Please, Please stay a night. I enjoyed to ride, but would not want to do it in one day. The GC deserves at least one night. The colors change from dawn to dusk. The colors change each day. I have always felt sorry for those who take a bus trip to the canyon, get there at noon and leave a few hours later. They have missed it all. Doing the GC in a day is like those tours that take you to 19 countrys in a week.