For the languages I've studied (Hindi, Mandarin, Esperanto (don't ask), Spanish), I've found that it's only a couple months before I run into a brick wall that simply requires lots of verbal practice with real humans in real situations. As such, if you're bound by shyness (like I am, somewhat) you'll find it very difficult to progress beyond a certain point.
I really like the Praxis language resources for learning. ChinesePod worked really well for me, and they have a program where you can hire a virtual language coach, find Skype buddies to practice with, etc. Probably the best you can do short of living immersed in the language. You can get a lot for free, too, though it seems like they change their pricing plans fairly often.
As for musical instruments, I agree with deciduous: play every day. Also, play with people in different modes: informal jamming, formal practice-heavy music like Western classical, informal practice-light music like pop songs, bluegrass, celtic, etc. I find playing with people really helps me get out of funks.
Once you're pretty good at an instrument, you can probably take a 30 minute lesson here and there to get you over various hurdles. If you spend $45 every couple months and practice practice practice what you learn, you'll use your money a whole lot better than you would signing up for a weekly class for 6 months.