Reddit mentions of V-MODA Vibrato In-Ear Noise-Isolating Metal Headphone with 3-Button Apple Control (Black/Chrome).

I've purchased 5 new pairs of earphones this summer with prices for being between $60-$130 per pair. Below are my reviews for all 5 pairs. Some are noise blocking and some are not. Some are good for exercising while others are good for travel. Some are great for if you love heavy bass music and some are good for listening to talk-radio or podcasts. All of them are in-ear style earphones. I consider myself somewhat of an audiophile, and over the past 5-6 years I've cycled through countless different brand and models of earphones.

V-Moda Vibrato ~$130 : Sound quality is not good enough for this price, bass levels are a little too high and drown out other sounds, and V-moda has a reputation for their cords breaking at the ends and from the buds within a very short amount of time. I previously had the Vibe first and second generations, and although they look stylish, they had these design flaws and the cord broke within a couple months. They won't block outside noise. Don't buy V-moda earphones. There are far better brands out there and you can get much better quality for less money. 6/10 - this rating is quite generous but its because their lower end earphones are much worse.

Klipsch S4 ~$65 : For the price, these are a good pair of earphones. I use them for traveling because they won't be too much trouble to replace if something bad happens to them. They are nice-looking from a design perspective, and they will block a good amount of outside noise. The sound quality is pretty good for their relatively cheap price, and the bass levels are high, but its never going to overpower the other tones. The cord seems a bit thin and flimsy, but I've had no issues with that so far. These are also great for exercising, and can be worn in two ways on the ear: the normal way or you can flip them up and wrap the cord over and around the back of the ear for a more secure fit. I really like that aspect about these, and the only other pair that I'm reviewing that has this options are the Shure SE215's (see below). They also come with a nice selection of tips and a good carrying case. 8/10.

Etymotic MC5 ~$60 : I had heard and read a lot of great things about this company, so I decided to grab one of their pairs. They are known for their 3-flange tips. For me, these type of tips are nothing special. Actually, the small and medium tips didn't even fit in my ear (with every other company the small or medium tips fit me best) and their large ones barely fit. Thankfully they came with some foam tips that did fit but they are not smooth and are rather coarse and uncomfortable. There was only one pair of tips that worked well in my ears out of the 3 types of tips, and there was only one pair of the style that worked for me, while the others had 3-5 pairs. Anyway, with any type of their tips, the earbuds stick out farther than any other earphones I've had, so I didn't like the way they sat or looked when I wore them. Sadly, I was also disappointed with the sound they produced. There was almost no bass levels whatsoever, and their volume level is the lowest I've ever experienced... you need to have the mp3 player probably 30% louder with the Etymotic earphones compared to any others to have the same noise level. The only reason I kept them is because with seemingly nonexistent bass, they are good for talk-show podcasts and when I listen to NPR. The cord seems decent and sturdy enough, and they come with a nice case. Maybe their higher-end earphones don't have these issues, but for me, they were a huge disappointment. 4/10

Bose IE2 ~$100 : These earphones are perfect for not blocking all outside noise. I use them for exercising and running outside, and at work so I can listen to music or the radio while still being able to hear if someone is talking to me. These are their second generation and a design improvement on the tips makes them stay really secure in your ears while doing any activity. The sound quality is quite crisp with a nice range of tones and good bass levels too. They've got a stylish design and a unique black-and-white striped cord. They stay comfortable and secure in your ears for long periods of time are are well worth their price. The cord is durable and they come with a good selection of different sizes and styles of tips and include a nice carrying case. I think these are the best non-noise cancelling earphones available for a $100 budget. I'm very impressed by these. 9/10

Shure SE215 ~$100 : Saving the best for last. These are the nicest earphones in terms of sound quality, durability, and for blocking outside noise. These are perfect for any situation where you don't want or need to hear anything outside your music. Great for airplanes, long car rides, loud public places, studying, etc. I'll even use them to fall asleep when my roommates are still partying or being loud when I'm going to bed. When exercising, you can wear them pointed up, and have the cord wrap over and around the backside of the ear for a more secure fit. I like to use the foam tips: they're like the earplugs that you squeeze and put in your ears, and then they expand to the shape of your ear canal and block outside noise. As a company, Shure supply's almost every big name musician and performer at large large venue shows with both their high quality earphones and microphone equipment. They far exceed every other brand in terms of sound quality produced. For noise blocking earphones on a $100 budget, there's no reason to get anything other than the SE215's. They'll even replace them for free if you keep a receipt, and they've done this for me and other people I know with their earphones that have broken long after a 2-year period. I had the first generation model for a while and the cord malfunctioned and they upgraded me to the newer model at no cost. With this current model they've deigned the earphones so that the cord detaches from the buds at the base of your ear, so that if and when the cord breaks, you don't need to go buy a whole new pair, just replace the cord. This is also great for if and when you want to upgrade to their higher end models like the SE315, SE425, and SE535 (each higher number is about $100 more than the previous) because the cord works for all of the current SE series earphones, just swap out the buds on the same cord. Once you try any model of Shure's earphones, you will never want to buy another company's earphones. They come with a few styles of different tips, each in small, medium, and large, and their carrying case is quite nice. Ask anyone you know with Shure earphones and they will gladly tell how how awesome the earphones are. 10/10

TL;DR: for the best earphones on a $100 budget, either get the Shure SE215 earphones (blocks outside noise) or the Bose IE2 earphones (does NOT block outside noise).

The V-Moda Vibrato earbuds sound perfect for what you described. The bass is punchy, but doesn't overwhelm the mids or highs. They come with removable earhooks. The only problem is they appear to be discontinued causing a major price increase. Perhaps you could find a pair on eBay or Craigslist for a reasonable price. V-Moda makes quality headphones, I've owned a pair of Vibes since 2007, they're beat to shit but continue to perform perfectly. Good luck in your quest.

Yep that's them:
https://www.amazon.com/V-MODA-Vibrato-Noise-Isolating-Headphone-3-Button/dp/B00452V26U

They're not being made anymore.

These are great and definitely worth the $$$