Any version of Fluxx is fun. It is a (relatively) fast paced card game that is easy to learn. Because it is an easy game and usually plays rather quickly, you can play it more anywhere. The games themselves are fairly cheap (average of $15) considering. I say games because there are many different versions and each has a different style and feel. I personally love Cthulhu Fluxx because chaos and losing are a very active part of the gameplay.
If you want a more involved game, Settlers of Catan can be fun. It is a more intense game that involves focus and strategy that can take an average of a hour or two to get through. I personally think that it is a great game for testing out the waters of long, strategy board games. If you enjoy Settlers of Catan, you'd probably enjoy similar games. Speaking of which, Small World is similarly intense that there is focus and strategy needed, and can take a long time to get through. It can be a lot more fun due to a lot more variety possible during each game. You are unlikely to play the same game twice with Small World. However, this larger games come with a rather large price tag and are best as party games. They tend to lose their fun with less people, but can take a long time the more people you have. It is also a game you don't want to play with people who don't like losing.
King of Toyko is another party game, but has a slightly smaller price tag and can be played much quicker than the previous two games mentioned. It is a silly game of King of the Hill (if you are familiar with that), so usually you can expect laughter. King of New York is very similar, with some additional features.
Takenoko is a more aesthetically pleasing Settlers of Catan. It also, strangely, has a more relaxed feeling. While still being pretty high on the price scale compared to some games, it is relatively cheap compared to other large games. You'll also find that it tends to be a quicker game than the other large, strategy games.
Those are just some games simply off of the top of my head. There are a number of stores that allow customers to just test out board and card games, such as Guardian Games. I would check out to see if there are any stores like that near you, get a small group together (four tends to be the best number when testing games), and see what games you enjoy the most.
150