Let me invite you to take a look at the nestorgames collection. They can be carried away and stored easily, as they can be bent and squeezed. Moreover, they occupy very little space and they are very light (around 150 grams per game, or 0.33 lb).
It depends on what type of games you two enjoy. Mystery Rummy: Jekyll & Hyde is a great small game if you two enjoy card games and is one of my favorite games. Hive is small and comes with a vinyl travel case if you enjoy abstract chess like games. Fantasy Flight Silver Line games come in a real small box if you are interested in games that have heavy themes. My wife and I really enjoy two player Red November and Citadels in the FF Silver Line. Ingenious: Travel Edition is also a good choice that my wife really enjoys but it only take about 7 minutes after you get the hang of it.
Bohnanza is a must :) Also Fzzzt (literally a deck of cards), Rosenkonig (copy the grid onto a sheet of A4), Lost Cities (mentioned above, you don't need the board), Roma and Traders of Carthage (you can easily copy the board onto 1 A4 sheet), Cartagena.
I'd suggest looking into "Taluva" as well. It plays great as a 2-4 player game, i'm currently in love with it. The box is big, but you could take the tiles out and store them in a more space concious way. They won't get damaged, they are some of the sturdiest cardboard pieces i've ever bumped into. The game teaches really quickly and plays in under an hour.
I'd agree with the suggestion of Lost Cities. I've introduced that to my girlfriend recently (a long-time player of traditional pub games such as cribbage and dominoes, has also played Triv) and now she's very keen to play it whenever possible. You could also try Carcassonne (slightly bigger box, a bit more space to play), which I've also introduced my g/f to (she liked it but it hasn't got to her like Lost Cities has). Hope that helps.