In short
The Forbidden City holds nearly nine thousand rooms and housed twenty-four emperors. It borders Tiananmen Square, and Jingshan park just to the north gives the overall view for a few yuan.
The Great Wall is an hour and a half away: Mutianyu is restored and less crowded than Badaling, Jinshanling is wilder.
What it really costs
Beijing is cheaper than Shanghai for housing, with a twenty-five-line metro that makes a car pointless and costs a few yuan a trip.
Payment is by QR code almost everywhere. Linking a foreign bank card to the apps before you leave is the single most important preparation.
What nobody tells you
The Forbidden City requires a named booking, opening at 8pm seven days before the visit, and entry is with the ID document used to book. It is closed on Mondays outside public holidays.
Much of the Western internet is unreachable: search engines, maps, messaging, social networks. Whatever has to work is set up before you arrive.
Winter is dry and bitter, summer heavy. April–May and September–October are the two windows, and they are also the busiest.
