Well, if it’s supposed to be something new, then it’s no wonder really that you don’t know how to represent it as a goal (or goals), because you don’t know yet what “new” means. As far as I can see, there is no good way to get more concrete, since defining something more means also to limit the possibility space, which is exactly what you don’t want to do, if I understood you correctly.
So I would just have one beeminder goal “do new things” that is decidedly open and undefined, it’s basically just a goal in which I’d track “Did I do something new or worked on doing something new in the near future?”. And then I would have more concrete complice goals, which are related to actual more defined things that you want to do. E.g. going to the zoo: That should be a goal in complice, since there are some arbitrary tasks that have to be done and you want to track them in relation to the go to the zoo goal and not to an undefined do new things goal. At the same time you can ask yourself with the help of beeminder did I actually (work towards) do(ing) something new? If I actually went to the zoo, or hit a certain threshold that I feel is enough to count my work towards doing something new, I’d log a 1, otherwise a 0.
EDIT: Tried to clarify and also correct some mistakes. English is not my native language, for which I apologize.