I've been seeing more "pocket games" in recent years. Some are designed to be both small and short (play in the time it takes for your food to arrive at a restaurant, for example); others are a little longer. Board Game Geek has a user-curated list of pocket games; some of them won't meet your needs but others might. For a trip like yours, I recommend avoiding anything in the Tiny Epic line; those games have lots of small plastic customized pieces (easy to lose, hard to replace). On the other hand, card games like Sushi Go or Point Salad would work so long as you're not concerned about moisture damage to cards. For something with a little more strategy, San Juan is a card game based on Puerto Rico. (You mentioned a deck of playing cards, so I assumed cards would be ok.)
Dice games like Yahtzee (mentioned in another answer) are compact. Roll Through the Ages, an "abstraction" of Advanced Civilization that plays in about half an hour, involves more strategy than games like Point Salad. It uses dice, paper scoring sheets to track progress, and small peg-boards to track resources, but those peg-boards could be replaced with any method of tracking how many of each of six different things you currently have. Dice in different colors would work.
Games like Nine Man Morris, Hnaftafl, and Fox and Geese require small markers and a board. The board doesn't need to be rigid; you can draw or paint the board layouts on cloth. I did this for a gaming event where I needed a lot of copies of these games and needed to be able to pack them easily. For markers, you can use any small plastic "stones", beads, or similar that will stay put without rolling; take some spares, and if you lose a few, no big deal. (Pennies also work.) One possible downside is that these are usually two-player games.
All of the games I've listed are fairly short and not very complex. Complex board games tend to come with lots of stuff, in my experience. Maybe your group could choose one game that's a reasonable compromise of bulk/weight and complexity and, if necessary, distribute the components? A game like Power Grid (choose one board) or Settlers of Catan or Eurorails could probably be managed in this way.
I hope after your trip you'll tell us what worked for you.