Are you trying to use your Pi as if you are a customer who comes into the shop and want to use their "Free" WiFi whilst you drink your coffee as someone else with (only) a laptop or smart-phone or tablet might do? In the same way as some authors write whole books in Coffee Shops there are Software developers who work the same way - and if you are working with a Pi you may even get an audience who wonder what that little box with the lights on it is for...
Plugging the Wifi Dongle of the Pi into the laptop (disabling any other built-in to the PC) temporarily and logging into the Wifi (and accepting the Sign-in Web-page that comes up in the PC's browser) will teach their system the dongle's MAC address, if you then deactivate the dongle (probably via a PC system tray icon) you should then be able to un-plug it and move it to the Pi and start that up. Some Free Wifi places like that allow more than one device to be associated with your free account, and if you are lucky they may allow more than one of them to be active at the same time in the same place. However you will probably want to have a VPN set up between your devices as such Wifi systems are not considered "secure" - e.g. Windows Firewall has special setting for "Public" Wifi setups so that things that you might share with other hosts on your home LAN are locked down on a public one.
Whether you will get twice as many adverts sent to you via EMail as the price of this remains unclear - there is no such thing as a Free Lunch (and Free WiFi may have its costs as well!)
EDIT: Silly me, forgot that properly set-up with the right keys shared between hosts SSH will provide a secure link between your Pi and Laptop. Also you will probably need to do the Windows equivalent to the Linux sudo nmap -sP 192.168.0.0/24 | awk '/^Nmap/{ip=$NF}/AA:BB:CC:DD:EE:FF/{print ip}'
(replacing 192.168.0.0/24 with something that describes the LAN that the units are on and AA:BB:CC:DD:EE:FF with the MAC address of the Pi's Wifi dongle) in order to find the IP address to use to SSH into your Pi...