St. George Utah Temple
Assembly rooms were the main feature of the first temples but most modern temples do not have one. Even in the temples that do have them they are rarely seen and rarely used. I have been to the Salt Lake, Manti Utah and Logan Utah temples multiple times. All three have assembly rooms on their top floors but I have never seen them. On the other hand my current temple, the Nauvoo Illinois Temple also has an assembly room. Since it is on the ground floor, just beyond the recommend desk and its doors are kept open, I have seen it. However the only time I have been inside was while on a temple cleaning assignment. My understanding is that Nauvoo's assembly room is used by the temple staff for meetings and devotionals. Perhaps the other assembly rooms are used in a similar way.
The Church built the early temples (Kirtland, Nauvoo and St. George) as sacred spaces primarily for gathering and secondarily for ordinances, they built the next few (Logan, Manti and Salt Lake) primarily for ordinances but still with an Assembly Room gathering space. Finally they built later temples, starting with Laie and with the exceptions noted in the last paragraph, exclusively for ordinances, meaning no Assembly Room.
The Kirtland Temple was the first temple that the Church dedicated in this dispensation. Because the Lord had not yet revealed temple ordinances the Church did not design It for the presentation of those ordinances but instead as a spiritual school and gathering place. It consisted of two large assembly rooms, one on each floor with pulpits on both ends (Library of Congress has a floor-plan). However, as described in my post on ordinances, Joseph Smith performed an early, preliminary version of the endowment there to a few people (Church History in the Fullness of Times: Chapter Twenty and LDS Living: What We Know About the First Endowment in the Kirtland Temple).
Nauvoo Temple
Similar to Kirtland, the Church built the original Nauvoo Temple with two assembly rooms, but added a baptistry in the basement where the Church first performed ordinances for the dead in a temple. They also divided the attic into rooms for the endowment ceremony and performed 5,634 endowments for the living there, along with 2,000 sealings for the living. (Deseret News: Nauvoo Temple Timeline and Church Historic Sites: Nauvoo Temple) The Church did not perform either endowments nor sealings for deceased couples in the original Nauvoo Temple (Temple Records of The Church of Jesus Christ of Latter-day Saints). However, they did perform sealings of living persons to their deceased spouse (Richard O. Cowan; Temples to Dot the Earth, pg. 60).
Similar to Kirtland and Nauvoo, the Church built the St. George Utah Temple with two assembly rooms. However shortly after dedication they partitioned the lower assembly room into rooms for the endowment ceremony. They also performed the first endowments for the dead in this temple (Church Historic Sites: Five Things You Should Know About the St. George Utah Temple and "Temple Pro Tempore": The Salt Lake City Endowment House). At the same time Brigham Young worked with other Church leaders to write down the endowment ceremony for the first time (Church History in the Fullness of Times: Chapter Thirty Two). During a renovation in 1937-38 they replaced the partitions with permanent walls and added murals (History of the St. George Temple pg. 70-71). In 1975 they renovated the temple to accommodate the video presentation of the endowment but kept the upper floor assembly room (St. George News: St. George Temple day; a significant, sacred beacon for over 140 years). The Church renovated the temple again in 2023, including the assembly room (Renovated St. George Utah Temple Ready for Tours photo 7/30).
Salt Lake Temple Assembly Room in 1911
The Logan Utah Temple was the first temple the Church built with four progressive Instruction rooms for the live presentation of the endowment, (see my post on Progression and The Church News: 135 Years Ago the Logan Utah Temple Was Dedicated, Here Are Some Fun Facts You Might Not Know About It). They Designed the Manti Utah Temple the same way. The Church originally designed the Salt Lake Temple (which was started first) with two assembly rooms. However, during its construction the Church altered the design by changing part of the basement and the lower assembly room into progressive Instruction rooms (BYU: Design Construction and Role of the Salt Lake Temple). All three temples still have assembly rooms on their top floor (ChurchofJesusChristTemples:Temple Designs).
Idaho Falls Idaho Temple
The Church designed the Laie Hawaii, Cardston Alberta and Mesa Arizona temples without spires or assembly rooms, and the Idaho Falls Idaho Temple with a spire but without an assembly room in an effort to make them smaller and less expensive (Design of the Cardston Temple). Since then they have only built four temples with an assembly room: Los Angeles California (Improvement Era: The Los Angeles Temple pg. 805), Washington DC (Model of the Washington DC Temple Interior on Display), Portland Oregon (The Trumpet Stone: LDS Temple Assembly Halls), and Nauvoo Illinois (Nauvoo Illinois Temple Floor-plan).
Therefore the following temples have assembly rooms: St. George Utah, Logan Utah, Manti Utah, Salt Lake, Los Angeles California, Washington DC, Portland Oregon and Nauvoo Illinois (The Trumpet Stone: LDS Temple Assembly Halls).