Like someone mentioned, the 28-70 is a solid lens, but I am gonna go against the grain here. If you are worried about balance and sticking to a budget, I have been incredibly happy with the Panasonic Lumix S 20-60mm f/3.5-5.6. It is way more affordable and honestly more reliable for travel because it is so light and compact. The 20mm wide end is basically essential for Tokyo architecture and tight streets, and the AF has never given me any issues on my fp body. I prefer this setup because it is a safe bet that wont break the bank or your neck after ten hours of walking. You can usually find it way under your budget too... which leaves more cash for food and experiences. It works well and I have no complaints about the performance at all.

OMG Tokyo is gonna be so sick!! You are gonna have the absolute best time with the fp because it is so discreet for street photography. I saw your post this morning and totally feel the panic lol. Quick question tho before I go off on my favorites... what kind of stuff are you actually planning to shoot most? Like are we talking mostly bright daylight street scenes or are you gonna be hunting for those moody neon Shinjuku vibes at night? It makes a huge difference for which direction you should go since that body can be picky with certain glass. Honestly just stick with the Sigma brand zooms. They are doing amazing things with their smaller series right now and honestly you cant go wrong with any of their glass that is built for compact bodies. They just balance so much better than the big chunky stuff. Just make sure its from their lighter lineup and youll be golden!

I've been using the Sigma 28-70mm f/2.8 DG DN Contemporary on my fp for a while now and honestly couldn't be happier with it. It's super light for an f/2.8 lens and doesn't make the setup feel front-heavy at all. AF is snappy enough for street shots in Tokyo too. Picked mine up for around $800, so it fits your budget perfectly.