e.g: Nodame Cantabile, Paratzzi (???)

Any genre, but nothing too melodramatic / depressing

Any type :B

Boss & Me, My Best Ex-Boyfriend, Best Time, Go Lala Go 2, Just You, It Started With A Kiss and its sequel They Kiss Again, Love You You, Our Times, Material Queen, Prince Turns to Frog, Rich Man Poor Woman,  Rock n Road, Sophie's Revenge

Not sure which goal you wanted but I basically listed down the movies and dramas which had the heroine working towards their own goals haha!
Hmmm, just not goal to get a man. Like their dream kind of goal :) But thanks! :D
Here are two more!
My Lovely Girl: The female main character wants to become a song writer. (Note: The drama has been quite criticised and not everyone likes it, but I found it quite cute and enjoyable, so it's up to you to judge if you might like it too or not :P)
Sassy go go: The female lead does everything to fight for the existence of her dance group (featuring the school's worst students), even if it means working together with the school's best study group, which they don't like(and neither do they).

I'd say that both of the lead females in A Man's Story have pretty independent goals that they're working towards.  At least for large parts of the drama.  And the goals are not so happy that I would call them "dreams", but they both have pretty good reasons to be doing what they're doing. Also the drama is not exactly a happy one, lol.  But I wouldn't call it depressing either, and it's definitely not melodramatic.

The Musical is pretty much the story of the lead girl trying to break into musicals, so there's that too.  Take it as such, and not a drama about a musical, and it's not even a bad drama.

Actually, there are probably a number of dramas that are similar to The Musical (and Nodame), with heroines working towards careers in the music or entertainment industry.  There's also What's Up, for example (reminds me that I never finished that one).
Thank guys! But how about non-musical theme? :) In anime, like Haikyuu (Sports, be his best, defeat superiors), Hunter X Hunter (Shounen adventure axn, finding father), Death Note (investagation, very smart use logic i like thinking, as long as the charact are likable)
Perhaps these then?
Gokusen: a yakuza heiress wants tobecome a high school teacher (if you like it, there's also Gokusen 2 & 3, and a movie)
Hitsudan Hostess: even though is deaf, the (female) main character wants to become the number one hostess in Ginza. It's really a great story :)
Yankee-kun to Megane-chan: a girl who used to be a deliquent tries to step awayfrom her past and become a good student & class president.
Thanks! :D I just added the two, but I'll pass Gokusen bec its too comedy