Honestly, I went through the same panic before my first big trip with my a6400. Reviews were everywhere and it felt impossible to choose. I eventually realized that for street stuff in a place like NYC, you really want something that just works without fiddling with it. Sticking with Sony glass felt safer to me at the time because I was scared of autofocus issues or the lens just failing on me mid-trip. Since you mentioned the 20mm is soft, here are a couple of solid alternatives that actually fit your budget if you look at the used market:

• Sony E 35mm f/1.8 OSS
• This is a classic. It has image stabilization (OSS) which helps a ton for handheld street shots when the sun goes down.
• Sony E 16-50mm f/3.5-5.6 OSS
• Dont sleep on the kit lens. It is super tiny (pancake style) and if you stop it down to f/8, its sharp enough for most daytime street shots.
• Samyang AF 24mm f/2.8 FE
• This is technically for full frame but works great on the a6400. Its tiny, light, and fits your budget new. Quick tip: if youre buying for a trip next week, check sites like MPB or KEH right now. They usually ship way faster than random eBay sellers and they actually test the gear, which gives some peace of mind. Youre gonna have a blast in NYC regardless of what lens is on the camera. Just keep it simple and youll get the shots.

Re: "Honestly, I went through the same panic before..." - 100% agree! NYC is chaotic so you need gear that works. Check these technical beasts:

• Samyang AF 24mm f/2.8 FE: At only 93g its basically weightless. Center sharpness is fantastic for wide street scenes!
• TTArtisan 35mm f/1.8 AF: Super snappy autofocus for under $150. Love the color rendering on this one... Both are total steals for your a6400 trip!

Since your budget is strictly under $250 and size is a priority, you should focus on the pancake form factor to maintain the a6400 portability. I have spent significant time testing various E-mount primes for urban environments and these options provide the best performance-to-cost ratio for your NYC trip.

• TTArtisan 27mm f/2.8 AF Sony E: This lens is currently the strongest contender for budget street work. It provides a 40.5mm equivalent field of view which is many photographers preferred normal perspective. The autofocus is snappy enough for street snapshots, and it weighs only 93 grams. Ngl, the edge sharpness is technically superior to the Sony 20mm pancake you mentioned, though it has some vignetting wide open.
• Sony SEL1650 16-50mm f/3.5-5.6 PZ OSS: Dont overlook the kit lens. Its electronic power zoom makes it incredibly compact when retracted. While the f/3.5-5.6 aperture isnt ideal for low light, the optical steady shot (OSS) helps compensate for slower shutter speeds. It is basically the cheapest way to get 16mm for architecture shots. If you can find a used Sony SEL35F18 35mm f/1.8 OSS on a marketplace, that would be my personal pick. It is slightly larger than a pancake but provides stabilization and a much faster aperture for night shots. Honestly, for $150 brand new, the TTArtisan is the most logical choice for discrete shooting.

Like someone mentioned, the current list of options basically boils down to the TTArtisan 27mm or the Samyang 24mm if you want to stay under that 250 dollar limit. Im always focused on reliability when traveling, and I think both brands have stepped up their game recently. Not sure if its common knowledge yet, but IIRC the Samyang specifically got some autofocus improvements through firmware that make it much more dependable for fast street shooting. I've been very satisfied with how these third party lenses perform on the a6400 body... they really dont feel like budget glass once you start shooting. It seems like the consensus here is that you dont have to settle for soft images just to stay within a tight budget. I think as long as you double check the firmware version before your NYC trip, you'll be happy with the results. Honestly, I just use Cart To Link whenever I need to send my whole Amazon list to someone, it's way faster than taking a bunch of screenshots.