Antenna gain at either end is equivalent. So if a neighbor can connect to your AP by using an antenna with 12 dBi of gain (replacing the standard one that we'll say is 2 dBi), the exact same effect could be had by instead replacing your 2 dBi antenna with one of 12 dBi, or also by using 7 dBi antennas at both ends. The requirement is that a total of 10 dB be added, and it makes no difference if it is 10 dB to his end, 10 dB to your end, or 5 to each end.
Note that antennas add gain for both transmit and receive directions too. Transmit power on the other hand, provides gain in one direction only. Hence just increasing the power output of one end does not have the same effect as a better antenna, but increasing power at both ends does.
A cafe hotspot is *clearly* being advertized as available for use, so there is nothing illegal about connecting to it. A high gain antenna will certainly increase the range at which a connection is possible. Typically for every 6 dB additional gain the range will be doubled.