Hi, I received a lot of recommendations for noise cancelling ear buds, and the one that popped up most often was Bose QC35. Unfortunately, it also seems that those are a bit out of the $150 price range (but some said there might be after market available). In any case, the responses are tallied below, and many thanks to all who responded.
Brian
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I had two sets of noise cancelling headphones, one Sony, one Bose quiet comfort 35 II. The Sony sounded good when playing music and were cheaper, but the Bose are vastly better at suppressing background noise. In my limited experience, if suppressing background noise is needed, then your sister should try to avoid making a false economy. She can probably try the QC35 in a shop. They are astonishingly effective.
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These are considered the best noise isolation earbuds: https://isotunesaudio.com/collections/earplug-headphones
I didn't buy because of the difficult shipping to my country and finally I bought beyerdynamics DT770M which are only isolating headphones (not cancelling) but I can say that they are the headphones for me in order to work quietly in office.
Anyway this is only my personal point of view, lot of people prefer small earplugs instead of cumbersome overhead headphones, so I really suggest to visit the site above where you can find the product for your sister.
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We evaluated the attenuation provided by Etymotic HF5 noise-isolating earphone (cost < $150) in a sound-attenuating chamber using three different ear tips provided by the manufacturer. We measured speech recognition thresholds (SRTs) using spondee words in the sound field with both ears of the subject plugged by the ear tips. Four participants were evaluated. The eartips evaluated were the Etymotic Research ER38-15SM 3-Flange Ear tips (size small), ER38-18 Large 3-Flange Ear tips, and the ER38-14F Standard Black Foam Ear tips. The foam ear tips provided the most attenuation, which is approximately 20 dB.
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I use a pair of Bose QC35 to shield myself from the NYC rumble and I'm very happy with them. But... they're over your specified budget, probably because they are wireless. The wired version, the QC25 costs ~$180 in the US, which is closer to what you're looking for. A lot of brands have noise cancelling models these days (Sennheiser, Sony, etc,), so it's worth looking around.
That said, it's also worth bearing in mind that noise canceling headphones are especially good at removing low-frequency relatively stationary noise (like traffic and airplane "hums"), and less good and removing high frequency non-stationary sounds (like speech) - so depending on the source of noise in your sister's office the headphones will have more/less effect.
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I have the same problem as your sister.
I know it's above 150$, but I got Bose QC20 noise canceling earbuds for my bday and they are just amazing (250$).
I also tried my colleague's Parrot Noise canceling headphones, and they are nowhere near as good.
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Sadly for your wallet, ANC is really where Bose shines. They're generally overpriced, in my opinion, but not in the case of noise cancellation. The QC35s come up for sale fairly often, so you might be able to get close to $150.
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I tend to like the sound of Audio-Technica headphones, and they now make a few noise-cancelling versions that are cheaper than their Bose or Sony counterparts. For example:
https://www.audio-technica.com/cms/headphones/c4ca191ebf334d8f/index.html
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Not science but I have been using the HF-5 (and pre-cursor) for airplane travel for the last 15 years and I love them. I also have the much more expensive Bose NC headphones but I find the Etymotics are much better for listening to a movie on the plane.
I use the foam tips mostly.
(as the in-ears are most effective in higher frequency but the active noise cancellation is more effect in the lows, putting the Bose OVER the HF-5s is amazingly quiet J)
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On the plane, I use a pretty low tech approach. I like to wear standard phone ear buds with hearing protection style muffs on top. The hearing protection muffs give around 30 dB protection across most of the spectrum. At the hardware store, the muffs typically give attenuation ratings vs frequency in their specifications on the packet. If you get a version with deep shells, then the ear buds don't even touch the sides.
It may look a little excessive in an office environment !