There is a lot involved here and we don't really know you or your background. I suppose the key here is for you to have an idea of what topics you have to cover and for you to understand that developing your design skills is a process.
To be a good designer you have to understand how the eye and mind is attracted and pulled by color, typography; and the balance and rhythm created by the placement and proportion of visual items. You will not become a designer over night - just as a designer cannot learn HTML and CSS overnight or the intricacies of producing something that works.
The short answer is one cannot be an expert designer and an expert front-end developer at the same time. But everyone can expand their skill set which is what I think you're trying to do.
So what should you do? Wow. There are so many places to start. The classes at Lynda.com are excellent. It's well worth the $25/mth. Take beginner design courses; take typography courses; learn color theory. If you're working on sites with tons of data then Tufte is a perfect bridge between the various worlds
Eventually you may also considering reading up on UX and IA. If so look up Krug, Jakob Nielsen, Donald Norman. Those names should be enough to take you down the UX rabbit-hole.
Check out these courses on Website/App design on CodeSchool, it might help you. They are complete and show you how to choose the correct fonts, colors, and layout, according to wich type of website you want to build.
You can also pay to have more, but I didn't have the occasion to try it out.
I guess I can't give you any personal advice, because your question is quite vague...And we all have our vision of beautiful websites