How do I connect with an Israeli community in Tacoma

I really don't know of an Israeli community. You could call the Synagogue for some ideas.

Temple Beth-El is the local Jewish temple in Tacoma. Services are Friday evenings at 7:30, with the exception of the last Friday of the month where services are at 6 pm. You can do a search for Temple Beth-El in Tacoma, and then go to the contact information page.