I don't have a ready answer, but here is a big collection of information I've told others when they've asked.
It depends on what level of work you are reaching for. Are you:
I expect, from having talked to several alumni, that the entire process will work better if you can find at least one other educator to work with, either from within NITARP or external to it. And, if you have regular meetings (weekly, biweekly) via phone, Skype, Google+, or whatever; it will keep the pressure on to make steady progress (as opposed to all in the last week) and you will help each other stay on track. You can approach whoever you want, however you want, though suggestions have been made that people could post "want ads" on the NITARP list, e.g., "I worked in 20xx with scientist y on topic z, and I would like to work on a similar project with someone else; is anyone interested."
If you do find someone else within NITARP, however you find them, if the complete "new to science" aspect is less important than the discovery of doing it yourself, if that other person was from a different team and/or different year than you, you can 'trade' projects. You work through your project from one of your years, seeing if you can reproduce (or improve upon!) your original results, teaching the other person (+their students) your techniques. This will not be linear; you *will* make mistakes as you go along, but hopefully you will not be as much at sea as you were the first time through (because you already know where you got trapped in error before), it will solidify your skills better, and you will learn entirely new ones from an entirely different project from the other person. And at least one of you has a sense of what the answer "should be", or at the very least "what we got before". You may very well have new data and new techniques to answer the questions better now than you did before. (ex: for IC 2118, my team worked hard to get a ton of Spitzer data. WISE now covers the whole sky at 3.5, 4.6, 12, and 22 um -- fewer bands than the 7 photometric bands of Spitzer, and lower (worse) sensitivity and resolution, but still, new data over a larger area. The "best practices" for finding YSO candidates have also changed since then -- different color selection schemes are used now. You could go back and see if you can reproduce our results from before, and/or find new YSOs.) From a purely selfish perspective, I would love it if you could put the icing on the cake and actually write up your work in the form of a distributable laboratory exercise...
If you can't find a partner, and/or the "entirely new" aspect is really important to you, you can find a recent paper in the literature and see if you can go and reproduce their results, or carry them further. Or pick a recent NITARP team's results and see if you can reproduce that work, and carry that further. There are some papers for which this is not appropriate, but there are others where you could at least attempt to reproduce part of their work. Not everything that gets published is right, so you might very well find errors.
If the "new to science" aspect is really important to you, if you do want to do something that will result in an AAS poster that can stand in the science sections, you will most likely need to find a partner (again, to keep the pressure on through regular meetings and to keep each other on track), and probably a scientist to check in with on a monthly basis. That scientist can help you come up with an idea.
There is also an option that is intermediate between the prior two paragraphs -- do what you did before but in a new region, if that's possible. My teams tend to look for YSOs in a star-forming region. So, if you don't care whether or not someone else has already done an analysis of Spitzer data and/or WISE data, you can go through the Messier catalog (or, for that matter, APOD) and pick any star forming region. The famous ones are observed by Spitzer for sure, and WISE covered the whole sky, so they're all in there. You can do a similar sort of YSO search as to what we did but in a new region. Some regions haven't been analyzed this way in the literature, but most of the Spitzer data have. The WISE data are newer than the Spitzer data, so there are fewer projects thus far that incorporate the WISE data. However, you may need to dig quite a bit in the literature to find these prior analyses, and that may not be your primary goal in taking on this project. If you are aiming for an AAS poster, though, that part is critical, because the chances are excellent that you will run into one or more of the astronomers who already did that analysis, and they will (justifiably) give you a hard time for not searching the literature first.
If you want to get some data into the classroom (not necessarily NITARP-related), we have a list on our website of all the programs we know of that help get real data (and analysis) into the classroom. The list is so long it has to be sorted by wavelength and it is international, so some resources are only available, e.g., in Australia. But most of them are US-based. Some of these programs might provide ideas. For example, there are two very rich repositories of labs, one for Chandra and one for SDSS. They have some canned labs which you can extend to other projects. I am trying to set up NITARP tutorials on many of these other opportunities and repositories.