Look, if you're hitting Tokyo, you're gonna be doing a ton of shooting at night. Shinjuku and Shibuya look incredible but the street lighting can be tricky. I'd strongly suggest you grab the Sony E 11mm F1.8 instead of the zoom. The f/4 aperture on that Sony E PZ 10-20mm F4 G OSS is gonna force your ISO way too high once the sun goes down, making your footage look grainy and mushy. You mentioned the warping on the 11mm. It's real but manageable. Just be careful not to keep your face right at the edge of the frame. Keep yourself centered while vlogging and the distortion isnt actually that bad. Plus, its super lightweight which matters when you're walking 20k steps a day in Japan. Budget-wise, you can usually find the 11mm for around $450-500 new, or even cheaper if you check the used market. Since you're on a $500 limit, that leaves you a little leftover for a decent ND filter for daytime shots. If you really want to save money, maybe check out the Sigma 16mm f/1.4 DC DN Contemporary Sony E. Its a beast in low light and very sharp, but fair warning, it is way heavier than the Sony options. For a vlogging setup on the ZV-E10 II, I'd personally stick to the Sony 11mm for the weight savings alone. Make sure to test it out before you fly so you get used to the framing.

I was honestly pretty let down by the zoom when I was shooting in the Golden Gai alleys. The f/4 is just too slow and the noise ruined everything... unfortunately. Since you're on a budget, look at the Samyang AF 12mm F2.0 E instead. It has better center sharpness and the f/2.0 handles the Shinjuku neon much better. You can usually find it under $350 and its a much better value.

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