I ended up getting Traveller's through Geico. Just want to post my story in case it helps others make a decision.
I called a few places and ended up picking Geico because they were the cheapest. They actually don't do renter's insurance - they use Traveller's for renter's insurance. Interestingly, Geico had a better price using Traveller's than calling Traveller's directly. I asked for the minimum level of coverage, which was $15K, and then I added on my wife's ring as a 'rider' to the plan. I learned the term 'rider' during my research and it essentially means that I'm covered for $15K + the value of the ring. Total cost I believe was $125 for the year.
Experience with a claim:
We had a "flood". Came home to our apartment to find that the drip from the faucet in the bathtub (that the super never got around to fixing) turned into a full stream of water (even though the handle was turned off). Although the water was going down the drain and not flooding the apartment, it was hot water. A week straight of basically taking a hot shower caused the whole place to turn into a sauna. The steam filled the apartment and created condensation on the ceiling and walls that dripped onto EVERYTHING, and as you can imagine, mold was everywhere. The couch and beds were ruined. Tons of clothing was moldy. The table and chairs had white fuzz growing on them. The place was gross, smelled terribly and was 100 degrees. Unfortunately, my wife was alone when she entered the apartment for the first time and boy did I rush home when I got her call.
For the next 3 weeks, we lived at my mother in Jersey. The landlord had no emergency number, so the water flow wasn't stopped till the next morning. He had no interest in cleaning up the apartment other than painting over "some" of the mold. Painting over mold doesn't fix it, especially when you work on just a few visible spots. He wouldn't pay for professionals to come in.
I learned that insurance only covers your possessions and not the property, so we would be on our own to get the place tested for mold and properly cleaned up. We opted for moving out. Anyway, on to the matter at hand - the insurance.
Traveller's was great! The day after I called, they sent down a representative who was very friendly. He actually told me he got into the business thinking that he's supposed to deny every claim, but was pleasantly surprised to find out Traveller's helps out a lot. Of course, that could just be talk, but I can vouch for it! He took note of everything that was ruined and which things he would pay for cleaning before replacing - for example dry cleaning costs before giving us money to replace the clothing. It took another 2-3 days, but then he emailed me an estimate where I had to update the estimated life of the different items. Once I put that info in, it took another day or two and he sent me the final amount based on their computer program calculating what items were lost and what their value was after depreciation. A check was cut and we received it shortly thereafter! I then brought in ServPro to come and clean our chairs, table, and dressers in the hopes of salvaging them - b"h they were able to be cleaned. ServPro wanted to charge me a lot for the cleaning, but I convinced them to only charge me the costs of cleaning those items that Traveller's estimated and paid me for. I don't remember exactly how this worked out, but not everything was included in the first check I got, and so they sent me a second check probably a week after the first one for the final balance. That second check also included a few hundred dollars for "getting dehumidifiers" which the agent told me he was able to put on the estimate to help with some of the cost of getting mold tests, etc. - things he wasn't allowed to actually put on directly as they related to the structure/dwelling and not my possessions. That was really nice (especially since we didn't end up getting mold tests done).
All in all, the experience with the landlord and not living at home and moving to a more expensive apartment was annoying, but surprisingly, the insurance was the best part!
