Sound dampening like bose headphones
Is it possible to create a system of noise canceling like bose
  headphones without say the headphones but instead wearable speakers or
  strategically placed speakers?


No, not really. The sound from an interfering noise source may have a particular repetitive waveform shape at distance X but at distance X +/- 1 metre the waveform shape can look (using a microphone and oscilloscope) a lot different. 

Consider a 1kHz sinewave - it has a wavelength in air of \$\dfrac{340m/s}{1000 Hz}\$ = 0.34m.

If you had a microphone at X and a 2nd microphone at X +/- 0.17m, the 2nd microphone waveform, displayed on an o-scope, would be 90 degrees shifted: -



The green image is the original microphone output at X and the red image is X +/- 0.17m.

What about wall reflections? They are going to disrupt things even more - there will be positions, in a typical room, where complete cancellation of the pure tone will occur in one ear but not the other.

What about complex sounds containing many, many individual sinewaves? I'm going to have to say "forget it". Headphones work (reasonably) because the measurement point of the noise, the ear and the re-injection of the cancelling signal are all fairly close and their relative distances don't change much at all.

Say you managed to position wearable speakers around you that kind of worked, what sort of sound would the person stood next to you hear? As sure as I can be, the person stood next to you would hear the original interfering sound and the sound from your speakers. They won't cancel out for someone in a different position.

Does it get better at higher frequencies? No it gets worse because the wavelength is smaller and the positional accuracy needs to be tighter.

What about the interaction between your left ears noise cancellation system and the right ear cancellation - there is no segregation between left and right without fairly decent headphones.