Jerusalem and the Old City are great places to walk around but there’s also a Jerusalem underground (not to be confused with the light rail :-) ). Remember that in archaeological sites as you go to lower layers you go back in history, for example, under Damascus Gate from the Ottoman period is the Roman gate to the city from the time of Hadrian. Not far is Zedekiah’s Cave, also known as Solomon’s Quarries, a 5-acre (20,000 m2) underground meleke limestone quarry that runs under the Muslim Quarter as far as the Sisters of Zion. According to legend, King Zedekiah escaped from the Chaldeans who had surrounded Jerusalem by fleeing through the cave all the way to the plains of Jericho.
If you like caves, there is also a very fine stalactite cave not far from Jerusalem, Soreq cave in the Avshalom Reserve that you can visit about 2 km from Beit Shemesh. Since you will be nearby this would be a good opportunity to visit Tel Maresha and explore underground, the caves, columbarium and tombs from the Hellenistic period.
Herodium has a series of tunnels dug in the mountain during the Great Revolt and then extended during the Bar Kochba Revolt. Near Herodium in Nahal Tekoa the Haritoun Cave is great for spelunking.
In the Jewish Quarter go underground to the Wohl Archaeological museum to see the remains of mansions from the Second Temple period. You can also take a guided tour of the Western Wall tunnel (you must reserve places in advance) that uncovers the part of the western support wall of the Temple Mount built by Herod that runs under the Muslim Quarter. Afterwards walk down the Via Dolorosa and enter the Sisters of Zion to see the Lithostratus and Struthion pool, from the time of Hadrian.
If you like tunnels, exit Dung gate and walk over to the City of David. There you can walk underground in the passageway from the Canaanite period – then you have 2 options: 1) walk the Canaanite tunnel (dry) and exit in Area E park 2) wade through Hezekiah’s tunnel (wet) and exit at the Byzantine Siloam pool. This site contains a lot of history and archaeology and is worth doing with a knowledgeable guide.
Theses are some ideas for exploring underground Jerusalem. Contact me if you would like me to take you exploring.