Anime has a wide variety of cute.
If you want a good romance I would recommend Toradora. The first five anime are streaming at anime news network and you can watch the rest for cheap (14$ for the entire series). It starts out pretty light hearted but gets more dramatic later on (I cried lot watching that one). It is not however nearly as soap opera like as shows like Air where it seems everyone has a terminal illness. It is only subtitled though so if that is a problem then it may not be for you. Chobits is an above average harem show the comedy drove me insane, but when it gets serious it has some thing to say. Full Metal Panic! has a good mix of romance, action and comedy. Minnory Days is another silly brainless romantic comedy (the humor drove me insane but I know a lot of people liked it). Fruits Basket is the definition of a feel good anime and will make you feel better regardless of what kind of day you had. Oran High School Host Club is very funny and has some good romantic development.
There are the slice of life anime. These are episodic and have little or no plot. Azumanga Daioh and Bamboo Blade do this without too many anime references. Lucky Star and Genshiken are fun if you can deal with a lot of anime references many you will probably not get. The Melancholy of Haruhi Suzumia has a lot of slice of life elements, but has more of a plot. It is not as deeply invested in anime culture as Lucky Star, but its still pretty nerdy.
If you want Yuri I would recommend Strawberry Panic. It can be a little slow at times (but not as slow as Maria Watches Over US the other big yuri title). It has some funny parts, but can get pretty sad too (a little bit like a soap opera). El Cazador De La Bruja is also a good yuri, but is also very action packed so if you want a break from action it may not be for you. Strike Witches also has some strong yuri elements though not very well developed. It is more of a fanserive action comedy (the fanserivce is too much for some people in that show).
If you want some pure comedy I would recommend Sgt. Frog (the fumiest anime I have ever seen). Hitalia is also funny.