Did you mean after Epsiode III or Episode II?
If you meant after Episode III, then I assume that ity would just go back to being a rather backwater, isolationist planet like it was before the Clone Wars. It isn't located in a place that would give it much strategic value, so I don't seen any real reason for the Empire to want it. And the Empire doesn't have too much control in the Outer Rim, so it wouldn'y make sense wasting resources defending it. But on the other hand, I suppose the factories could have been converted to produce something for the Empire and the Empire would enslave the Geonosians to work them.
The same kind of thin could be said about Naboo, or any PT/CW planet really, just cause it was important once doesn't mean it always will be. If you put it in earth terms, Kosovo and Yugoslavia were all over the news for along time several years ago, nowadays you almost never hear about them in the news, but it doesn't mean that they are no longer there. I think the same thing happened to Geonosis, with the CW over, people simply didn't care anymore and it just drifted back into obscurity. The galaxy is a huge place, I bet the only reason most people have heard of it is because the CW started there. If you were to ask most Americans to name every country on Earth and find it on a mp without names, not too many people could do it. And there are only about 200 or so countries on earth, there are supposed to be 1000's of planets in the Republic, and 1000's more that are undiscovered or independent.
Now if you are talking post Episode II, I'm going to have to agree with Jesse.