What will we see between the CMB and the current oldest object seen? The cosmic background radiation (CMB) is estimated to be from 13.7 billion years ago (BYA), and very shortly after the big bang compared to that time frame.  The oldest coherent objects we've detected are around 500 million years after the big bang, making them 13.2 BYA.
If I understand these stories correctly, that means that we have not yet detected any radiation that can be clearly identified to be emitted from a source between these two times (otherwise NASA would announce an even older discovery).  I don't think that that is implying that there's nothing there to see, although it's obviously the case that it is beyond our current technology to see in that window.  The severe redshift and small solid angle are two complicating factors, another is that most galaxies were only beginning to for around 13.2 BYA.
Regarding astronomical objects of ages between 13.2 and 13.7 BYA:


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*What is there to see?  Obviously, the 13.7 BYA point has the problem of near homogeneity but what about the times in-between?  Are there cosmic structures that we could see there but no where else?  Things that predate proto-galaxies?  After the CMB, did matter stop radiating?  Are there other near homogenous emissions we could look for?  Does that make any sense?  What is an accurate characterization of that time frame?  Does physics make good predictions for astronomers to chase?  What discoveries in that time frame are next?

*What telescopes will see them?  The record holding earliest protogalaxies I reference are highly red-shifted light and the CMB is $cm$ wavelength.  Would new discoveries in this time frame mostly be in-between those two wavelengths?  Are there promising telescopes that might open up new areas of study here?

 A: 
The period between the CMB redshift ($z_\text{CMB}\approx1100$) and the current record for highest redshift objects known (either GRBs or galaxies in the Hubble Ultra-Deep Field, about $z\approx9$) is when the first stars are expected to have formed. They probably start forming at redshifts in the somewhere in the range $15$ to $30$, maybe larger. It's a big unknown at the moment. Either way, these ages correspond to roughly 13.4 to 13.6 Gyr lookback time but the exact timing isn't precisely known.
In this range, we'd expect to see the first stars and the first (proto)galaxies. The stars (and associated events like supernova/GRBs) are therefore there to be seen and, since the high-$z$ protogalaxies we know of are already looking quite galaxy-like, there are probably others out there at slightly higher redshifts.
At higher redshifts than $30$, things really do become dark, though. That's why we call this period the "dark ages". The gas in the Universe cools because it's no longer ionized and therefore mostly transparent. It only starts heating up again when self-gravitating structures begin to contract and collide.
Based on this...

  
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*What is there to see?

Up to $z\approx12$, maybe more extended protogalactic structures, like those in the Hubble UDF. Up to $z\approx30$, there should be metal-free stars and (shortly after) their associated death-throes. At higher redshift the Universe is genuinely quite dark, though.

  
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*What telescopes will see them?

The James Webb Space Telescope is partly designed to see these high-$z$ objects. Its wavelength range is roughly 0.6 to 28.5 microns. The first stars are expected to emit mostly ultra-violet light. At redshift $z=14$, say, a 0.1 micron UV photon would be redshifted to 15 microns, squarely in JWST's range.
A: Well, we have to rely on theory here. The $\lambda$CDM model  predicts that there should be lots of hot optically opaque hydrogen forming into the first stars and galaxies. Particular objects of interest will be the Population III stars which formed and died very quickly.
The best eyes on this scene in the near future future will be the JWST and the E-ELT. Both should have the power to see the first galaxy formations but not the wavelength range to reach much further back...
