I worked for over15 years in South Asia and East Asia with various government agencies and NGOs and I have always been impressed by the LDS Church's charitable relief efforts. When disaster strikes, they are among first ones in - and they come with appropriate aid.
For example, we watched as container after container of LDS aid arrived in Indonesia after the big 2004 tsunami, and again after a big earthquake in a different part of the country the next year. We were in China following the 2008 Wenchuan earthquake in Sichuan and again the LDS were busily bringing in supplies. I can't remember a typhoon in the Philippines in the last 10 years where I haven't run into LDS relief efforts.
I was discussing the LDS with some of my classmates who work in the US and they tell me they regularly see hundreds of LDS volunteers (sometimes called Mormons) in yellow vests working in the aftermath of disasters in the US like hurricanes Sandy and Katrina.
One of the things that impresses me most about the LDS church's relief efforts is their attitude. They don't try to limit their aid to their own adherents, they are willing to help where help is needed, regardless of religion. It doesn't even matter to them whether they get "credit" for their efforts - only that the aid gets to those in need.
For example, in Pakistan after the 2005 Kashmir earthquake there were problems with local officials who were very opposed to their people finding out that relief supplies were coming from Christians (to the point that the officials were blocking shipments to starving people), so the LDS simply had their supplies repacked to remove any mention of the church so they could get through. One LDS leader told me "It's only important that the hungry are fed and the homeless are sheltered, not that we get our names in the papers". I heard a similar story from a colleague that the LDS have been quietly shipping food to North Koreans on the same "no name" basis - politics don't matter, only hungry children matter.
I saw criticism of the LDS church several years ago for a "lack of transparency" (echoed in some other reviews on this site) and I did some research of my own.
Apparently the LDS church doesn't file the same financial disclosure documents with the US IRS that big US charities do (like Red Cross), but I learned that most US churches aren't required to file them and therefore don't file either. I also learned that the LDS church has a modern internal audit department and that one of the major public accounting firms (currently Deloitte) audits the church and its internal processes and auditors.
I looked into the governing board overseeing LDS charities and it is quite impressive (and a bit eclectic, which I like), including a Stanford business school professor, several university presidents, a state supreme court judge, and even the former chief pilot of Lufthansa, All serve as unpaid volunteers.
LDS charities distribute 100% of funds donated for relief. An LDS church leader told me that their charitable relief funds are separated from the church's other funds (like their tithing program) by a one-way gate. The church can use other funds to support relief efforts (like paying for all the overhead of the relief program), but no relief funds can be used for anything other than relief aid.
Given what I have seen and experienced personally and what I have learned about them, I would be very comfortable recommending The Church of Jesus Christ of Latter-Day Saints as a worthy charity.