Generally speaking, two doses of the MMR vaccine as a child is considered sufficient evidence for lifetime immunity in the States. However, immunity can lapse, so it's a good idea anyway to have your titers drawn to see if your level of antibodies is enough to still be considered immune. If they show a deficient level of antibodies, then you just need a booster of the MMR. It happens: I was 26 when I had my titers drawn and discovered I did not meet the threshold to be considered immune for measles. I wasn't expecting that, but it was no big deal as I just had to get the MMR once more and that was that.
As for Israel: I wouldn't call it an outright outbreak, but there are increased numbers of cases over there. These seem to be restricted or at least concentrated to the ultra-religious communities, which makes sense as they have a denser population density (bigger families and a lower willingness to move away). Most vaccinate but an unfortunate amount still are skeptical, which explains why herd immunity is seemingly failing in these communities. Most of Israel isn't experiencing measles, so depending on where you are going depends on your level of potential exposure. Still, you have to fly there, and that alone can be exposure enough (as an Israeli flight attendant's exposure and very adverse reaction has made the news). You're not likely to contract it in Israel, statistically speaking, and that is true if you limit yourself to the secular spaces like Tel Aviv; however, even the non-religious love to visit packed spots like the Western Wall so I'd just make sure you're still considered immune. It's a good idea regardless.