Q:

What is your workflow for "don't care" photos?

Let's say you've got a set of photos in a trip and, apart from a few really noteworthy, all others are nice photos, but not so much for you to spend a lot of time processing on them. In such circumstances, what is your normal workflow (I am particularly interested about LR4 with or without Nik Software)?

A:

I'm not sure I ever have images I truly don't care about at all. I'm always for keeping them or against keeping them, at least.
My System
I use stars and flags in Lightroom:

Reject: Photos I will be deleting as soon as I complete the current pass, if I'm at home.
I defer deletion when I am working away from home on a laptop. I wait until I have merged the on-the-road library with my main home library and backed that up before I delete anything from the laptop. Two is one, one is none.1
★: Ugly photos which I have to keep for some reason. They may be poorly composed, ill-conceived, out of focus, under/overexposed...
A special class of ★ photo is the purely documentary photo, such as those of tourist attraction signs. They go with a set of photos taken at that place and serve only to document the shoot.2 Such photos are never worth showing to others in their own right.
Another example is the gray card or color balance card shot you take at the beginning of a session and between lighting/scene changes. You have to keep the shot at least until everything is color- and white-balanced, and you might want to keep it for future reference purposes.
★★: Technically acceptable photos which are nevertheless unattractive.
An example of such photos are my home inventory pictures, and a lot of family and snapshot work.
Most such photos have inherent value for me only. I rarely show them to anyone else.
★★★: Good photos. The meat-and-potatoes of my library.
This is probably as close as I get to "don't care." These photos are in focus, well-composed, and attractive enough to avoid dropping to a ★★ rating. 
Yet, I don't spend much time on them, because I show them to others only when I don't have a ★★★★+ photo to serve the same purpose. If they're seen at all, it's usually only as narrative glue in slide shows.
I rarely do more than crop & straighten ★★★ photos or apply batch changes with Ctrl/⌘-Shift-V. When I do spend more than a few seconds on such a photo, it is in an attempt to raise them to a ★★★★+ photo.
This is my threshold for off-site backup. Except for home inventory and family photos, I don't bother to include ★★ photos in off-site backups, and I don't back-up ★ photos off-site at all. The idea being, if my house is hit by a meteor, I won't drop any tears over losing such low-rated photos. I'm willing to keep them around as long as it's "free," but I'm not going to pay off-site storage fees to maintain their existence through a disaster.3
The "middle" photo of an HDR set is usually ★★★, since there has to be enough beauty present to be worth attempting an HDR. Yet, there must be room for improvement for the same reason: if the middle shot is ★★★★★ in its own right, why bother with HDR? The under- and over-exposed shots in the set get rated ★ or ★★. If the HDR conversion improves the shot, it gets rated one or two stars above the middle shot. If the experiment fails, I toss everything but the normally-exposed "middle" shot.
★★★★: Great photos. These are photos that make me happy enough that I'm willing to show them to others without reservation.
Such photos appear in web galleries, slide shows, etc.
★★★★★: Perfect photos. These photos are beautiful, well-lit, properly composed, and usually technically flawless. Occasionally a photo's uncommon beauty will allow me to accept it into this rare set despite small technical flaws.
Such is the beauty of photos in this rarefied class that I will display them long-term, knowing that I will not quickly tire of them. These are the photos I hang on walls and use as desktop backgrounds.

The higher the rating, the more redundant backups I have.4
In my system, every photo gets a rating or gets rejected. The only photos that are unrated are those I've imported but haven't yet bothered to make a decision about. I have a Smart Collection that warns me about such photos, reminding me that I have to do something about them.
If you find yourself with months-old unrated photos, either give them a token rating (★) or give them the boot. You clearly don't care enough about them to do anything else.
My Workflow
I call my workflow for getting photos into this scheme THE CHAINSAW. Think of a chainsaw ice sculptor: he starts with a big block of unformed material and his job is to rapidly cut away everything he doesn't want.
In Lightroom, go to the Filter Bar and click Attribute. Clear any settings that may be here already, then click the middle of the three flags (unflagged) and set the Rating part to "equals no stars." Then save it as a Custom Filter, calling it THE CHAINSAW. I put it in all caps because I use it on every import, so I want to be able to pick it out of the list instantly. Plus, chainsaws are dramatic. (Feel free to pronounce the name in your WWF announcer voice.)
In a folder of unprocessed photos, activate THE CHAINSAW (tthbbitrrrrrrr!), then turn off all the UI distractions by pressing F.5 All you should see is the first "undecided" photo in this folder, full-screen.
Now put your fingers on the 1-4 keys and your thumb on the X key.6 Taking at most a few seconds per photo, rip through the set, giving them an initial rating or rejection. Trust your expertise and go with your initial "flash" impression. If you find yourself dithering, it's probably a ★★★ photo; rate it and move on.
When all the photos are rated or rejected, delete the rejected photos: Ctrl/⌘-Backspace.7
Turn THE CHAINSAW off with Ctrl/⌘-L, then press F to leave no-distractions mode.
Then go back and start working on the ★★★+ photos. If there are a lot of them, do the ★★★★★ photos first, then ★★★★. Spend time on ★★★ photos only if you still have time left or find yourself needing a filler of some kind.
Some photos may increase by a star or two after being edited. This should not worry you. Your initial flash impression was correct.
That we deleted the trash without attempting to rescue anything first is also not a problem. We can't expect more than a few stars of improvement, which isn't enough to bring a zero-star photo up to the level where we would really care to spend time on it in the first place. You'll find people who will tell you to keep absolutely everything, just in case, but I believe these people are packrats. Yes, technically there is a bit of ore there in the tailings pile, but it's not worth the time and effort it takes to refine it.
Excepting those that are part of an HDR set, ★ and ★★ photos never get any more attention at this stage. I typically put off HDR experiments until after I've gotten through the ★★★★+ photos at least.
Finally, I run my various Publish Services for on- and off-site backups, empty the Trash/Recycle Bin, and erase my memory cards. I may also schedule an on-exit catalog backup via Catalog Settings at this point.

Footnotes

I don't erase my filled memory cards on the road for the same reason.
This the sort of metadata we had before GPS tagging.
Low-rated photos do still get backed up locally, such as in whole-HDD mirrors.
I don't literally have 5 levels of redundant backups. I just mean that there are more copies of my ★★★★★ photos floating around than copies of my ★★★ photos.
In Lightroom 4 and earlier, F had a much more limited (though related) function.
The equivalent in those older versions is Ctrl/⌘-Shift-F, E, T, L.
I don't bother dedicating a finger to the 5 key since ★★★★★ photos are so rare. Stretching from the 4 key is easy.
Defer as above if your backup methods are not available where you are working.

A:

"Don't care" photos? I don't edit them at all, so the only way they factor in my workflow is that I don't flag them with anything. Why spend time on something you don't care about? I'd delete them, but then again, I'm a digital packrat who only throws away really bad photos, such as badly focused ones.
Maybe you meant photos that are good but not great? Those, I usually just crop and sharpen, plus a bit of color correction and curves as needed.

