Pandemic Legacy is great - it is a collaborative board game that you play over the course of a year - with each game representing a month in that year. You get the chance to play each month twice, so if you don't beat the game on your first attempt of a particular month, you can try again. What you do in one month will affect how the game plays in the next month - it's such a clever game and comes with all these little boxes that you open up as you progress in the game. They change the rules and objectives permanently. You can practise the game as many times as you want by playing it as regular Pandemic before you dive in to the legacy version. The rules are quite easy to learn. It's really fun playing a collaborative game for the first time if you have not done it before.
Splendor is easy to learn and great fun. We have Marvel Splendor, which is for 2-4 players. You collect tokens to recruit different characters to your team, and once you've collected a particular set and accumulated enough points you can win the game. There is also Splendor Duel, which is specifically for 2 players. I've not played it but it is supposed to be really good. Splendor is also quite easy to learn and doesn't take long to play. (Much less time than Monopoly!)
You might also like Ticket to Ride, where you compete against each other to build the best train routes. Sounds really dull but it honestly isn't!
I also really like Parks. You can play it solo or with others. It's based on the US National Parks and the artwork is stunning. It also has really nice wooden and metal components. You are hiking through trails and you collect tokens that you use to pay to visit various national parks, which are worth points. There are other things you can collect that increase the number of points you can score - it's really clever. You play the game in a set number of rounds and at the end of the round, the person with the most number of points wins. It's fun to play solo too.
Also check out Cascadia if you like nature games. Very beautiful game and easy to learn.