When we visited my husband's aunt & uncle in Rechovot 3 years ago, they took us out for lunch at the cafeteria at Weizmann. There didn't seem to be a requirement of a connection with the Institute. The food was surprisingly delicious, and it was fun to watch the students, etc. It was not full of tourists, and my teenagers enjoyed being at the school. It also was reasonably priced, which is why our older relatives go there regularly.
Other than that, our uncle made great turkey schnitzel for dinner.
Have a safe and wonderful trip, p.j.