I'm with @DWKraus that there's no absolute right, and I think @Chenmunka's link gives guidance, particularly the non-accepted answer: sometimes there are specific reasons behind mixed tenses.
When I imagine your first example as a narration, the 3 sentences do feel like you start "inside" the story, then make an aside from "outside," then re-enter. As if:
Beijing is the capital of China. (I enjoyed my time there.) Her wide boulevards are...
I would say the "specific reason" you did this might be because you want to begin with an emphasis on the city of Beijing. Imagine alternatives:
I enjoyed my time in Beijing, the capital of China. Her wide boulevards are...
That starts outside and goes in, avoiding the flip flop, but doesn't have the same emphasis.
Beijing, the capital of China. I enjoyed my time there. Her wide boulevards...
That just obfuscates whether you're inside or outside, and wouldn't work unless you happened to like the style.
And so on. If no alternative delivers the emphasis you desire, then I'd argue that that is the specific reason to justify the flip flop.
Interestingly, this would resolve naturally in languages with different orderings. In Korean for example your second sentence can begin with the location:
베이징에서 즐거운 시간을 보냈습니다.
Beijing, in, enjoyable time, I spent.
This simultaneously delivers emphasis and begins "outside" the story, going in. Any emulation of that in English might sound unnatural, or weird if you kept structuring it that way.
Beijing, I enjoyed very much. It is the capital of China. Her wide boulevards...