Space Center is designed to provide cities with extra tourists, max tech level for industrial buildings, and to be fun to look at.

Construction

Space Center costs 1,000,000 simoleons to start construction. Once construction starts, you will need to fill the construction resources from your city: 40,000 Computers, 1,400 Alloy, 170,000 Fuel. The entire region can chip in to finish construction.

Operation

The Space Center has a power requirement of 100 MW/hr which MUST be "available to trade" from the cities in the region. This question here goes into the detailed analysis of how operating requirements work. The Space Center also requires 300 spare workers to operate. This is crucial and will frequently cause the Space Center to stop working if the Sims decide not to commute anymore. Since jobs in the current form of SimCity are so easy to have unfilled, it tends to cause underemployment and thus no free sims to work at the Space Center.

Space Center's Two Phases of Operation

1) "Building" Phase

Immediately after completing the construction, on the bottom left you will see a countdown timer saying "Building Satellite. You have 48 hours left to launch". This timer is notifying you that you are in the first phase of operation.

2) Launch Phase

After the 48 hours has ticked by, you will need to wait another 24 hours for the actual satellite launch. These two phases will keep rotating, Building then Launch.

After the countdown is complete they will wheel out a rocket and it will launch, notifying you:

Benefits

While all the launch hooplah is purely for visual entertainment, what's going on behind the scenes during these phases? There are two benefits:

1) Tech Level

This benefit is pretty simple and straightforward. It acts exactly like a University in that it upgrades any Industrial zoned buildings you have to the highest tech level. I didn't personally study or watch how fast buildings would get upgraded to the highest tech level but I assume this Great Work would upgrade them rather quickly for its high cost. The tech level benefit from the Space Center is visually represented as purple lines stretching out everywhere in your city:

2) Tourists

But you wouldn't build the Space Center for it's tech level benefits, you would build it for the tourist benefit. In the particular region I built this in we had no Tourist cities so I don't have any hard numbers on its full potential. The biggest thing to remember is the tourists come in phases. During the 48hr Building Phase, your city will not receive any new tourists. During the 24hr Launch Phase, tourists will start to flow in. These two phases will repeat indefinitely. I need to do some further testing regarding the Wealth classes of Tourists it pulls in (I suspect all), and see to how many tourists it truly could attract.

Security Incident

There is a random event built into the Space Center that causes it go offline due to a "security incident". There is a mission that pops up saying they require Computers (just one shipment) to get back running. I didn't wait for a very long time to see if it would just have went away, and I didn't cancel the mission. This is disturbing since a shipment of Computers costs 150k+ simoleons, and the mission reward is 10k.

Conclusions

Due to the high cost of constructing the Space Center (I think I paid around 8,000,000 for the computers alone), it's financially not worth it at all. Even once you get it constructed it randomly will stop and wait for you to send it more Computers (which you could have made money off of). I did not maximize my tourism in my cities to see what the Space Center is capable of, but due to the high cost of materials, you are not likely to have much tourism in the cluster because all your cities will have to be either huge Oil/Metals/Electronics cities, or they will have to make solid money off tourism, and import materials to fund the construction.

It's pretty clear its not financially smart to build this Great Work. The real reason to build it is for purely for fun because it's pretty enjoyable to watch the rockets blast off next to your city. If I learn anything else I will update this answer.