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Ashdod has a long, pretty coast (8 km/6 miles) with several public beaches and a marina accessible to the public. Ashdod's beach strip is about 2/3 the length of Tel Aviv's, yet it serves only about 1/10 the population. Since it's not crowded or very touristy, it's a great place for a calm trip.
Jonah's Hill
Named after the prophet Jonah, who is believed to be buried here. It is the highest point of the city (around 150 m above sea level) with the city lighthouse on top of it.
Park along the southern bank of the Lachish river, which reaches the Mediterranean Sea here. In addition to the usual park facilities, it has a small zoo, and is a popular spot for birdwatchers.
The ancient port of Ashdod was here (the ancient city was further inland). You can see a large fortress several meters from the coastline. It was built in the 7th century and used until 1260. The fortress is impressive to see, but fenced off and you cannot enter it.
It's in the MonArt center, and has 13 exhibition halls. In an architectural echo of the Louvre, the entrance to the museum is through a glass pyramid.
A fountain in the Ashdod Sea Park close to the beach. Inspired by the Magic Fountain in Barcelona, this fountain puts on an impressive sound and light show several times each evening (except Friday night and when there is rain).
In modern slang, a "philistine" is a person without culture. But the ancient Philistine people had culture, and you can see it in this museum. Ashdod was one of the five main Philistine cities in the Biblical period.