I have a Chromebook I use more frequently when I'm out than I do my Macbook or PC laptops. I never have a problem connecting with my Chromebook, provided the place's WiFi is working properly.
Unfortunately, in my area, I find a lot of the public Wi-Fi networks are not working properly, but then I live in rural area, and I often am the only person in the place trying to use their Wi-Fi network. If I have problems, I usually ask someone working there if they can restart their wireless router and once they do this, it usually solves the problem. Other times, the employee rolls their eyes and says "Oh, it never seems to work." and then he/she mumbles something about "No one uses it anyway..." (Such is life in Podunk!)
I almost always have my phone with me, so I can try logging onto the network with it. Typically, if I can't log on with my Chromebook neither can I log on with my phone.
If I can't reach the connection page (like you mentioned in the OP), then usually the store's network connection to the outside world is completely down. A some places, that don't have a login screen, I often get a network connection but then the browser doesn't go anywhere when I type in a URL. In these cases, I sometimes find that switching to (using) "Google name servers" under the network tab solves the problem -- in other words the place's DNS server isn't working properly or hasn't been setup properly. See image below re: switching DNS:
So, you could try that. Click on the bottom right of your screen and then click "settings", then click on the name of the network, which will bring up the panel shown in the image above.
More detailed instructions here...
Frankly, I'd suggest asking the management of the place if they know if their Wi-Fi is working properly, or check with someone else who's in the store with a laptop to see if they have a working connection. Or, if you have a smart phone (or another laptop) take it with you and see if you can get a connection with it. Unless you verify the Wi-Fi is working properly, you'll just be spinning your wheels trying to connect.
For basic instructions on connecting to a network with a Chromebook --
go here -- or here (
Can’t connect Chrome device to the network).