Keep your eyes open for problems where you have to do some form of brute-force search. Those that doesn't have a clear solution other than trying all the possibilities.

Another thing is that the best kind of problem for SAT solvers are problems that ask a yes/no question. Is there a way to satisfy all the constraints, and if so what are the variable assignments that do so? It's also possible to use SAT solvers for other kinds of problems (e.g. find the solution with the best score) but it's more advanced.

Try CSP instead. It works as as higher level abstraction over SAT that is easier to model with.