I was in Tel Aviv in 2013 and other places in Israel.
I found the Diaspora Museum in Tel Aviv interesting and worth going to. It doesn't have a lot of artifacts, but the museum tells the diaspora story well through multi-media, models, story boards and through other means. It's on the campus of the University of Tel Aviv, which is 5 to 7 miles outside the city center. I took a city bus to the Diaspora Museum. It was the only museum in Tel Aviv I saw.
On the bus I met a professor of Yiddish Studies at the university. He spoke 5 or 6 languages, but English wasn't one of them. We communicated in Spanish.
I liked seeing Carmel Market, an open-air market near the city center. I bought grapes for probably $5, and the vendor gave me enough to feed a family for probably three days. I took me 10 days to eat them all.
Finally, I swam in the eastern Mediterranean Sea. As you see from my name, I'm in Chicago, where Lake Michigan is freezing for 11 months a year. The Mediterranean was like bath water. What a difference!
Just walking around central Tel Aviv is worth it. The city is very cosmopolitan. I loved it.
In Jerusalem, I saw three excellent museums.