The audio seems to be getting worse in this new material... or at least, no better :/
Wouldn't a better translation be 'I spend a day in the city'? Or is it used for both in Spanish?
The present tense (paso, in this case) means both "I spend" and "I am spending."
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This is a bit tricky. I believe the idea here is that you are spending the whole day (or at least a good part of it) there, and not just the current moment. So while grammatically correct, the use of the present progressive here would sound weird to a native Spanish speaker.