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I did a program called Discovery - that matches your description.

http://www.discovery-training.com/

The original course is one weekend, for three consecutive months. And then you graduate. Many of the graduates return each month for the Saturday night party or to volunteers with the program.

I've heard great things about Unitarian Universalist churches!

DH belongs to a unitarian universalist church (aka one of those non denominational churches). there are a lot of people that go there that do not believe in a god. they have groups that get together to do good deeds around the community & on occasion travel to work on larger volunteer projects. his has a food pantry in it where we volunteer. they do not subscribe to any doctrine other than their core beliefs (copied from uua.org website):
There are seven principles which Unitarian Universalist congregations affirm and promote:

The inherent worth and dignity of every person;
Justice, equity and compassion in human relations;
Acceptance of one another and encouragement to spiritual growth in our congregations;
A free and responsible search for truth and meaning;
The right of conscience and the use of the democratic process within our congregations and in society at large;
The goal of world community with peace, liberty, and justice for all;
Respect for the interdependent web of all existence of which we are a part.

@MamaMoose: a lot of people find as they get older they don't agree with parts of the religion they have grown up with, but feel that faith and spirituality is still important to them. nondenominational churches allow for everyone to maintain their own beliefs & allows for exploration into different religions without the judgement that there is one correct set of beliefs. scripture, from all different religions, can contain wonderful life lessons- even if we don't agree with the religion is originates as a whole set of beliefs. going to church allows people to spend time reflecting, sharing ideas & beliefs, and focusing on living a good life. church is also a social/community experience, a place where you share your joys and sorrows and seek the support of others. everyone who belongs to any church has found a purpose for it. one purpose can simply be that it gives them a place to belong, that alone can be a powerful thing.

I was raised a UU and they focus a lot on charitable work in the community and elsewhere. Some of the churches are very left in terms of political affiliation of its members, which can be a little off-putting in an election year, if you're not entirely on the same page. Some churches are very crunchy, but others are not, you just have to find one that you feel comfortable with. As for the religion part, it's open to all denominations, you believe whatever resonates with you. My particular church had hymn books and we did a lot of singing during services. I loved it!

There are groups like the Junior League that focus on volunteer service. There are also tons of local groups you can join on meetup.org that organize volunteer works, and all sorts of things.

As an athiest, I don't really think there are non-religious churches. Even the UU is still religious, even if much more inclusive than most other churches.