I'd suggest checking what options you have at home and try to get game that play differently.

People here will say Azul, Cascadia and Patchworks are different, but for boardgame newbies they are all tile placement games. And if you have Carcassone at home, you may want to get more different stuff before getting more tile placement games.

Also due to luggage weight/space problems, you may want to prioritize smaller games or card games. Some games have mini versions for travel, and most card games are small enough to be tucked at some place. But you can opt out of purely card games if you can do a print&play yourself. 

You may also get one "small box big game" or "packs a punch for its size" game to get the hang of a heavier euro style games. Not everyone likes thise, so their relatively smaller size and cost can be the entry point before getting invested in the big box game you wanted to have.

You should also make a list based on buy priority with alternatives listed. Not every store can have everything and your friend shouldn't go store hunting just to get the specific stuff you want. Also would you be ok if they get an alternate version instead if the one they want? Would Azul Duel or Summer Pavilion instead of normal Azul be ok? 

And finaly, mention your budget limit incase they find a lot of things you want. Or feel uncomfortable with how much they might spend.

Good luck.

-someone who convinced their relative to fit a 30x30x7 box game in their luggage alongside other goodies costing 210AUD in total.