You could say tameshite miru for "I'll try (it) out." Other than that, if you want to say "try X and see what happens," you would use Vte+miru (no kanji for miru); use Vou to suru for "try to do X."
E.g. Ano resutoran ni itte mimasu. "I'm going to try going to that restaurant." Or, more naturally, "I'm going to give that restaurant a try."
Nattou o tabeyou to shimasu. "I'm going to try to eat nattou." This gives the implication that you feel it will be difficult and that you aren't sure that you can do it, as opposed to just trying it out for the first time.