I'm far from an expert, but I'll answer your questions...
I never saw Blue Man Group, but my hairdresser did and she really liked it. She also liked Danny Gans, another one we never saw.
We never rented a car when we went. If you've never been there before, you can easily spend at least three days checking out the other hotels on the strip. There are buses that run the strip, that go downtown, for $2. We took that, our last trip, to Freemont Street. If you're planning on going to Hoover Dam or the Grand Canyon or somewhere other than the strip, you could rent the car for the day. The traffic is so bad on the strip, you could probably walk faster. We also took a bus to the Stratosphere, which is at the end of the strip. They have an observation floor there, with the two rides at the top...Big Shot and a roller coaster, but like someone else said, you gotta do Big Shot, but skip the roller coaster. The view at the top of this hotel is gorgeous. Try to get there for the sunset...beautiful!
I'm not a gambler but found plenty to do and see to occupy my time. Our last trip, we planned a few pool days and did the strip at night. We don't stay a week, though. Five days is long enough for us.