The following are open to my knowledge :
Halo Taiman- meat open till 12:30-1:00 Harav Machpud
Located at the entrance to the city at the gas station ( right outside givat Shaul)
Bar burger - meat open till 3 am Harav Machpud located at shumel Hanavi and Yoel
Caffe Rimon - meat Harav Machpud dairy mehadrin located in Ben yehudah , open after 12 however can close on occasion before 1
Mifgash Hashcia- pareve and dairy bakery style, mehadrin UNDER CONSTRUCTION AS OF NOW
located on Rechov Hillel and rebbi akiva open 24/ 6
Dr Toast - Dairy , Rabbi rubin , can be relied on till 130 open on occasion till 2
Located at shumel Hanavi and bar ilan
Dr pizza - Dairy , Mehadrin , can be relied on till 200 am INCL DELIVERY
With 2 location Hillel and rebbi akiva, and Bar Ilan and Adoniyahu With a Rabbi Rubin Hechsher
Pizza city - Dairy , Mehadrin , open till 130 ish , with 2 locations
Golda Meir and Bar Ilan , and shlomtzion Hamalka is open till 3am every night
Big apple pizza- Dairy , Mehadrin open till 3 am
Located in Ben Yehuda
Nechama Bakery - Full bakery incl pizza bagels and dips , with a Badatz
Open 24/6 Located on Rechov zonenfeld ( Bais Yisroel)
Pizza Hut- MEHADRIN , open till 2 am located at Shamai and Ben Hillel
Motzai Shabbos, and Thursday till 3am
Rechavya 25- Full service convenience store open 24/6 Located at Davidka Square and Hanaviem