Honest question: what are they gonna do once they find it?
Then after the party, everybody has the hangover that may never end, because finding the Higgs right where we expected it is potentially the worst case scenario: http://www.sciencemag.org/content/315/5819/1657.full
There are a ton of questions that Higgs cannot answer already and yet if we find Higgs precisely, research comes to a stop?
It almost feels like there's a split between theoretical physcists and everyone else, with theoreticians saying if you take away our broken toy, you better replace it with something we can play with!
Given Nature already trumped Einstein, his contemporaries, and all since, I think we can be fairly secure that we will ALWAYS having find something new to learn or discover from practical science.
After all, that's how we used to almost exclusively learn before scientists went a bit crazy with maths. These days there seem to be many more models out there than there is good science behind it - at least to a layperson like me. :)
This argument should also be read along with the fact that last I knew, none of the accelerators have been able to turn up anything else particularly interesting either. Some of the supersymmetry theories predicted particles in ranges that we should be able to see (barely) and none of them have appeared. We're down to hoping that there's something else to find in the extra room the LHC will give us at full blast or we really will be up a creek.
"These days there seem to be many more models out there than there is good science behind it - at least to a layperson like me."
And in fact your observation is connected; particle physics has been starved for data and in the interim have come up with all kinds of things, trying to find things that may have testable consequences. This would go a lot better with some data.
I know of only one, and whether it tests anything at all depends on which interpretation of QM you have. Based on a Geiger counter, either place, or don't place a heavy weight. Try to measure its gravitational pull regardless of what you do. It only measures a pull if you placed the object. If you believe in the Everett interpretation, this says that gravity, at least to a first order approximation, splits with the universe. We do not have sensitive enough instruments to measure non-linear differences from GR.
History tells us that theoretical science done in the absence of experiment is unlikely to lead to useful knowledge.
(especially question 7) will help, even though it does not give the name for such an experiment.
Four.
So, whether there's science still to be done and whether we'll ever be capable of building apparatus that can actually test it are two different questions. For instance, what if the next interesting thing post-Higgs Boson happens at energies 1000 times bigger? There's a good chance we'll never build an accelerator that powerful.
It is possible that we will discover new phenomena and new ways to test gravitational theories once we can observe gravitational waves. I expect we will detect gravitational waves in ~10 years and identify a specific source in ~20 years; sooner, if there are some powerful sources that we did not think of yet.