I've been thinking off and on a bit about what might work well as a restricted/limited space/indoor antenna. I stepped back and considered the basics:
If you have a wood framed structure with no large metallic materials, it should be mostly transparent to RF. If you're inside a structure, and that structure has significant metal (in the framing, insulation, or siding), it is going to act somewhat like a faraday cage. It will tend to block RF from outside, including the signals you want. I know that they're using metal studs in some residential construction now, and some insulation has a foil on one side. Those could cause significant shielding. It won't affect RF from inside, which probably includes the signals you don't want (RFI from appliances and such), so you'll still pick up your plasma TV.
One common rule of thumb (from a shielding point of view, where you're trying to keep RF inside a box, say for meeting RFI regulations) is that openings should be less than 1/20th of a wavelength. Note that this is a rule of thumb, not a hard number. For 6925 kHz, a wavelength is 43 meters, so 1/20th is 2.2 meters or 7 feet. So it sounds like a very large window may allow RF at that frequency to get in. It seems to me that if you have to keep your antenna entirely inside, putting it as close to (or on) a large window might help. I'm even thinking about running a loop around the perimeter of the window.
If you can get your antenna outside, that should help immensely, even if it is a small antenna. You're likely to pick up more of the signal of interest, and less RFI from inside. Of course if you have local RFI issues (like the streetlights and commercial signs Lex brought up), you're going to pick those up.
I'm fortunate to live in a rural area with a bit of land, so I've been able to install quite a few antennas over the years, of different types. I still can pick up RFI from various sources including neighbors' appliances, and things here in the house.
One thing that has become obvious to me is that loop antennas offer significant noise reduction as compared to dipoles and other antennas. I'm not referring to a loop that you can rotate to null out specific sources of interference, but a loop that is fixed in orientation. I'm not sure exactly what is going on, but my current line of thinking is that the loop tends to reject relatively local sources of RF because they induce common mode currents in the antenna that get cancelled out.
I've compared the loop antennas (I have a 132 ft T2FD that doesn't tilt as much as it should, and a 635 ft sky loop antenna that is at various heights around the yard between roughly 15 and 40 feet) to dipoles cut for individual bands. The dipoles produce stronger signals, but the noise levels are also much higher. The signals from the loops are lower, but the signal to noise ratios are fat better. To the point where I've discontinued use of the dipoles. The sky loop generally outperforms the T2FD except at very high frequencies, say 20 MHz and up. It's to the point where I almost exclusively use the sky loop.
Now, a 635 ft loop is obviously not practical for the apartment dweller, but it does make me wonder whether loops in general are the way to go (Lex mentioned that his best compromise is a small loop). The next question is, can anything be done to further improve things?
I feed all of my loop antennas with a balun. I find significant noise reduction, vs just connecting the coax to the ends of the loop. This might be a good test to try.
Getting the loop outside might be the next step. Could it be run around the outside perimeter of a window, in a relatively unobtrusive way? (This might not work well if the building has aluminum siding)