I can even tell you accurately that the house price in Xicheng is more expensive than that in Haidian.
Xuanwu house price will be cheaper, but it's far away.
If we consider the distance and house price, it must be Haidian District.
Of course, it is very close to Tiananmen Square, between Xicheng District and Dongcheng District, which is in the middle of Beijing.
The Temple of Heaven is in Chongwen District next to Xuanwu District.
What you said is centered on the west side. If you come to Beijing, you can visit Beihai, which is also a royal garden. Shichahai is located in Xicheng District.