After being a Buddhist for 12 years, I've taken an interest in Hinduism, specifically Advaita Vedanta and Vishishtadvaita. I feel that these lineages—and perhaps lineages I'm unaware of—would be a better fit with my current temperament and goals. I understand that you don't necessarily need to "convert" to Hinduism, but I'd still like to be part of a community to help aid my practice and navigate the scriptures.
I don't know your exact location in the US.
In Southern California one of the most popular Hindu organizations following Advaita Vedanta is Self Realization Fellowship of Paramahansa Yogananda. It is currently headed by an American, Brother Chidananda, and thus obviously accepts converts. You will find a lot of information in this web site:
I used to go to Ramakrishna Vedanta Center of Southern California which had many American born Swamis and Pravrajikas. I am posting a web site of Ramakrishna Vedanta Organization of Southern California where you will see photographs of one American born Swami and one Pravrajika and thus obviously accepts converts. You can find out the nearest Vedanta Center from them.
I am unable to give any references as to whether they accept converts. All I can say is that I have visited both organizations and seen lots of Americans.
Let me add that the most aggressive organization that actually converts is ISKCON. ISKCON does not accept Advaita or Vishistadvait Vedanta.