Late to the party but honestly Tokyo is a blast for vlogging so I get the stress. Before you drop the cash though, are you planning to use the gimbal for every single shot or do you want something light enough to just hand-hold? If you're worried about weight but still want that blurry background, the Viltrox AF 13mm f/1.4 STM Lens for Sony E is basically the perfect middle ground. It's much lighter than the Sigma 16mm so it wont kill your gimbal motors, but it gives you a wider field of view thats way more forgiving for vlogging. 13mm on the ZV-E10 II gives you a solid perspective where you can actually see the city behind you without it looking totally distorted. It usually sits right around $350 too, which keeps you under budget. Another solid shout is the Samyang AF 12mm f/2.0 E Lens for Sony if you want something even tinier, tho you lose a bit of that f/1.4 bokeh magic.

I actually tried running the Sigma 16mm f/1.4 DC DN Contemporary on a small travel gimbal last year and it was a total letdown. Unfortunately, the physics just dont work out well for vlogging. It weighs 405g and the center of gravity is way too far forward, which kept stalling my motors during quick pans. Not as good as I expected for a compact setup tbh. If you need that wide look but still want bokeh, look at the Viltrox AF 13mm f/1.4 STM Sony E-mount. It usually lands right around $400. Another option is the Samyang AF 12mm f/2.0 E. It is significantly lighter and way easier to balance on the ZV-E10 II. I spent way too much time fighting with my gear instead of enjoying the scenery on my last trip... you really dont want that in Tokyo.

Go for the Sony E 11mm f/1.8 Ultra-Wide Prime for sure! For vlogging on the ZV-E10 II, focal length is everything since Active Stabilization adds a significant crop. 16mm ends up feeling way too tight for arm-length shots in a crowded place like Tokyo. The technical specs on the Sony are just way better for your specific setup... it only weighs 181g compared to the 405g on that Sigma! A small gimbal will definitely struggle with the Sigmas front-heavy balance and weight distribution. I love the dual linear motors in the Sony too, the autofocus is basically instant for face tracking. Plus, f/1.8 gives you plenty of that creamy bokeh you want without the back-breaking weight. It fits perfectly in your budget too. Seriously, the portability is a total game changer for travel!