I went on a service program with Global Volunteers in Costa Rica some time ago. Our team worked with locals to build a school in the Santa Elena area. The work at that point was pretty basic - shoveling out the area where the foundation would be built, mixing concrete etc. A couple of older participants worked in the school library with the children.

The program fee included transfers from/to the airport and local lodging/food/transportation. We stayed in a local family-run hotel within walking distance of the project site. International airfare and optional tourist activities were not included. The organization is a 501c3 so I was able to take a tax deduction for the program fee and IIRC the airfare as well.

The weekends were free to explore - some people visited a volcano and hot springs, I went with others to the beach and went on a rainforest canopy tour.

They're not affiliated with any religious group and have programs all over the world, including the USA.