The silver dome contains a fully-automated photoelectronic meridian circle made by Carl Zeiss. I do not know what information can be got with this instruments, but I can imagine the system was very very expensive. The instruments are now not used, because more precise method using artificial satellites has been developed. It has been planed that the dome will be used as a museum. You may be suprized if you see the vast area in Mitaka.
Tama area is the name of the western part of Tokyo Metropolis. It consists of 26 cities, 3 towns and a village. A lot of people (about 4 milion) live in a eastern half part of the area. However, there are many mountains in the western part of Tama area, and there are very little flat land. Many hiking spots are in the western area, so you can enjoy walking on the trail, camping, and so on. If you see the beautiful mountain scene, you may not believe this is also in Tokyo.