Honestly I don't know of any other denomanation that has the sense of community that LDS has. I guess you could try Amish or Mennonite as they are pretty deep with community. Amish do accept converts(just really hard to convert since it requires taking up there lifestyle)
I was Roman Catholic, belonged to a non denomanational church and tried out Assembly of God, Congregationalists, Methodists, Baptist, Southern Baptists, , Nazarenes, Orthodox(can convert but they never treat you like an equal), JW, Church of Christ, Boston Church of Christ(scary), 7th day Adventists, Brethren and a number of non denomanational ones.
Of all those I never felt a sense of community. JW they all treat each other with suspicion which creeped me out. Orthodox is heavily ethnic based. Boston church of christ was basically a creepy cult. Basically it all felt spiritually dead. Many of them no one talked to each other, or only to there select group of friends.
I was also a Muslim for a few years, you first think there is community(for men atleast) but then you find out about the different cliques, people using you, fist fights in the masjid(mosque) racism,etc. I wouldnt want to be a woman convert(or revert as they say) with all the illegals wanting greencards, trouble making friends(compared to men) ect
I also tried out Bahai Faith and Hinduism Bahai Faith there is no sense of community, Hinduism there is alot of racism.
I'm an agnostic now but if I still believed in God I guess the only Christian church id consider belonging to is one of the Mormon sects. But you arnt for that so I guess the best thing to do is just do some research on different churches.
The person below me brought up the Espicopalians. Another spirutually dead church. Basically it feels like Roman Catholic. The one on my street uses all the local drug addicts and alcoholics to do little jobs for the church to get food and clothes but you never see them on sunday so it seems the church dousnt want them near the "clean" people.