This year (5778) the 22rd of Nisan falls on Shabbat. In Israel this day is Isru Chag Pesach (as opposed to the diaspora, where it is Acharon Shel Pesach).
Does one say Av HaRachamim?
On the one hand, we generally don't say Av HaRachamim when Tachanun is not recited (as it is not throughout Nisan).
On the other hand, many Ashkenazim make a point of saying Av HaRachamim during Sefirat HaOmer (due to the Crusades). Thus, on the following Shabbat (29th Nisan, Mevarchim Chodesh Iyyar) they do say Av HaRachamim, despite it still being Nisan and also Mevarchim HaChodesh, which is generally a reason not to say Av HaRachamim.
On the third hand, siddurim I've checked (e.g. the Artscroll "Lefi Minhagei Eretz Yisrael" siddur) don't list Isru Chag Pesach as an exception to the no Tachanun => no Av HaRachamim rule. Maybe Isru Chag is 'happier' than Mevarchim HaChodesh, like Rosh Chodesh Iyyar where they don't say Av HaRachamim if it falls on Shabbat, despite it being during Sefirat HaOmer?
On the fourth hand (and I'm not sure how relevant this is) in the Diaspora they will be reciting Av HaRachamim today, as Yizkor is said on Acharon Shel Pesach.
I'm running out of hands, so I'll stop here.