"Find your itch and scratch it". If you want it to be an enjoyable process, you have to find something you'll enjoy doing (sorry, bit of an obvious statement, I know).
Did you enjoy the game aspect regardless of your admitted lack of artistic skills? There are plenty of games of the intelligentsia style that don't require years of training at art school (Connect 4, Reversi/Othello, Checkers/Draughts et al).
I'm currently working on one game project for the kids at my 5yo son's school - it's a side-scroller that involves a few students and teachers and I dread doing the artwork. I'm hoping I can find a program on the net somewhere that will turn a photo into a Simpsons-style character, otherwise there's some local artists that have said they can donate a few pictures gratis.
However, that's been sidelined since my son has discovered Connect 4. Although I enjoy playing the physical game with him, I'm not always there. That is more suited to my own artistic skills which are probably on par with yours.
Other than that, you need to think of something yourself - what are your interests outside of computers? Play the guitar? Try a music composition program. Enjoy playing tennis? Come up with a social tennis membership/scheduling program.
Even if those programs are never used outside your computer, they're still useful for training you up in various aspects.
That's about all I can suggest without further information.
Following your comment that you're mostly interested in trying new languages, most languages fall into families. There's no difference between C and Pascal and FORTRAN and COBOL. It's the "whole different approaches" that differentiate them, such as:
- The procedurals such as Pascal, C, COBOL.
- The objects such as C++, Java, OOCOBOL, Python.
- The functionals such as F#, Prolog(?).
- Forth and Brainf*ck (with apologies to ChuckMoore :-).
If you find an family you want to develop further, it may be worthwhile asking a question specific to that family such as "What's a good program to write in F# to get experience with its way of doing things?".
Still, exploration is okay, but I'm not sure it would be enough of a driver (for me anyway) to make it truly enjoyable. I'd rather have a pressing need, business or personal, to make it worthwhile.