Japan is gonna be a blast but honestly, the wind in Tokyo and the constant city hum can really mess with your audio. I have spent a lot of time with the ZV-E10 and that side-flip screen is a total pain once you start rigging it up with cables. Especially if you are trying to move fast. If you are doing street interviews and walking around, here is how those options usually perform:

• Sony ECM-G1 Ultracompact Shotgun Microphone is okay if you absolutely hate cables. It is tiny and powers through the shoe. But ngl, the sound improvement over the internal mic is pretty minimal. It is mostly just better at rejecting noise from behind the camera.
• Rode VideoMic GO II Lightweight Shotgun Microphone is a decent option for the price. The problem is the cable. It definitely gets in the way of the screen. You can tuck it away with some velcro ties tho.
• DJI Mic 2 Wireless Microphone System is probably the most effective for noisy streets. Clipping the mic to your shirt means your voice stays clear regardless of wind or traffic. I would suggest the DJI for your specific trip. It is more versatile for travel. When you are in a crowded spot like Shibuya, a shotgun mic still picks up a ton of ambient noise because it is further away from your mouth. A lavalier mic near your collar just handles those environments better. Just make sure the receiver is positioned so it doesnt block the screen rotation... definitely test it out as soon as it arrives before you jump on the plane.

I've been looking over the suggestions and honestly, the MI shoe vs cable debate is the most important part here. In my experience with the ZV-E10, that flip screen makes cables a nightmare for fast shooting. Since you're doing street interviews in a windy place like Tokyo, you really need to get a mic off the camera and onto the person speaking. Shotguns are great but they pick up too much ambient reflections in dense cities. If you want to stay under budget, just go with a wireless lavalier kit from Saramonic. You can find their basic systems for way under 200 dollars. They offer much better signal-to-noise ratios for voices than a shotgun at a distance, and they basically eliminate the wind noise issue because the mic stays closer to the source. If you're dead set on a camera-top mic though, look into the Sony ECM range. Anything using the digital interface will have a lower noise floor because the A/D conversion happens in the mic, and you wont have to mess with those annoying wires blocking your screen while you're trying to frame a shot.

Following this thread

I definitely agree with the point about the flip screen being a major bottleneck for vlogging. I would suggest you be very careful with the Rode choice because that cable often dangles right in your line of sight when the screen is out. If you are doing street interviews, you might want to consider the Sony ECM-XYST1M Stereo Microphone instead. It is well within your budget and uses the Multi Interface shoe, which means no cables to snag while you are navigating crowded spots like Shibuya. One quick tip: if the wind is really hitting you hard in Japan, make sure to turn on the low-cut filter in the ZV-E10 menu. It helps the mic handle those gusts much better. Also, the Sennheiser+MKE+200+Compact+Directional+Microphone&linkCode=osi&tag=7649-20" target="_blank" rel="nofollow sponsored">Sennheiser MKE 200 Compact Directional Microphone is a great alternative because it is extremely short and much less likely to peek into your frame if you are using a wide-angle lens.

Any updates on this?

No way, I literally just dealt with this yesterday. Small world.

Building on the earlier suggestion, you really gotta prioritize that MI shoe connection or you will be fighting your gear the whole trip! I have used the ZV-E10 for ages and honestly, everytime I try to use a mic with a cable, I end up missing a shot because I am fumbling with that flip screen. I did a huge trip through Osaka and Tokyo last year and the Sony ECM-W2BT Wireless Microphone was a total lifesaver for me. It is absolutely fantastic because you just slide it on and forget it. No cables to snag on your bag! Basically the thread is saying cables suck for this camera and shotgun mics might be too noisy for street stuff. I totally agree. For street interviews, having a wireless clip-on is a game changer compared to a shotgun that picks up every siren in Shinjuku. Quick tips:

• Keep your audio levels around 10-12 so the loud Tokyo crowds dont clip your sound.
• Bring a tiny pouch to keep the receiver in when its not on the camera so the pins dont get bent in your bag. Seriously, go wireless for the interviews. It makes everything so much more fun when you arent tethered to the rig!