I was wondering if someone could recommend  some Taiwanese drama's? I'm very new at watching them as I'm trying to watch Love Around but it's  very slow. 

These are some of my all time favorite taiwanese dramas:

Autumn's Concerto - Romance and drama
Fated to Love You - Romance, comedy and drama
Devil Beside You - Romance, comedy and drama
It Started With a Kiss / They Kissed Again - Romance, comedy and drama
Mars - Romance, drama and mystery/physiological

I hope you can find some good dramas to watch! :D Good Luck!
Erm, for chinese dramas or taiwan dramas, it will be easier for you if you like a specific actor or actress, because there is just too many dramas, but noteworthy dramas to watch? 

Dramas starred by Hawick Lau, Hu Ge (his dramas.. ain't that nice as of late) , Wallace Huo (he is a damn good actor, whichever show he is in bound to have a good storyline at least, if not watch for the acting), Wallace Chung etc, 

there are more but these are the actors I am primarily always checking out their new project/movie. :)
I second MARS. I also recommend the movie Secret.
Fated to Love You and It Started With a Kiss are both pretty popular tdramas that I like.  My favorite drama actress is Rainie Yang so anything with her in it...Devil Beside You, Why, Why Love; Drunken to Love you, etc
It started with kiss and devil beside you are must watch!
i agree that you could start with It Started with a Kiss, and Devil Beside You.
then follow it with Why Why Love ;p

or maybe you could watch Meteor Garden. it started the F4
Most of the good ones have been mentioned but here's the ones I'd recommend. :)

Heartbeat Love
Autumn's Concerto
Tiamo Chocolate
CHOCOLAT
Devil Beside You
Why Why Love
Alice in Wonder City
Hi My Sweetheart
Just You
Love Buffet
MARS

Maybe Romantic Princess & When Love Walked In if you take them with a pinch of salt. :)
Autumn's concerto
Romantic Princess
Fated To Love You
Hana Kimi