Tel Aviv and Jerusalem restaurants
MarkC's Tel Aviv suggestions are all met with a huge +1000 from me! Brunch at the Brasserie is amazing. Manta Ray is quintessential Tel Aviv overlooking the sea. I'd add Nanuchka (Lilenblaum St.) for Georgian cuisine, and Agadir on the harbor for hands-down the best burger I've had yet in Israel.
If you want to venture to Jaffa, Dr. Shakshuka is a must. As is the Yoezer Wine Bar.
Chakra, on King George, they have a killer tasting menu and their menu changes monthly, so it's all seasonal goodies.
Machneyuda, Beit Yaakov St near the Machane Yehuda shuk. Call to make reservations at least a day in advance. Menu chages all the time. Trendy, fresh, amazing.
Cavalier, on Ben Sira Street. French with a Mideastern twist. Located in the "triangle" of the city center, you're within walking distance of anything you'd want to do/see post-dinner.
Adom, just around the corner in the Feingold Courtyard off Jaffa Street.
Mona, Shmuel Hanagid St, an absolutely adorable place in the old Artists' House.
Angelica - relatively newer Kosher restaurant on the pedestrian Shatz St.
Arcadia, 10 Agrippas St. - upscale Israeli, with a seasonal (daily) menu.
Shalom Falafel, on Bezalel Street. Doesn't match the "nice comfortable atmosphere" qualification but you'll eat the best falafel - either in a pita or flatbread - you've ever had.
On that note, if you're wanting authentic hummus, go to the Old City, avoid the restaurants that look like tourist traps (that is, the ones with nice umbrellas and signs in English), turn off onto a back alley (yes, it's safe) and practice your Arabic while sopping up warm hummus with warm pita bread. Abu Kamel is a favorite of mine, just up from the Mauristan church.
In my opinion, all restaurants in the Ein Kerem village are overpriced and only "eh." The town is worth going to, but save your appetite for a meal back in J'lem. If you must, there are two great ice cream places - Trezoro and Sweet ein karem.
Tel Aviv has such a huge and varied restaurant scene now, it's practically like New York or Los Angeles. For beach views - Manta Ray and Pini B'Chazer (good food also). For upscale, Mul Yam in the new Tel Aviv port, Toto and Herbert Samuel. For a "scene" go to Tapas Achad Aham and Brasserie.
Areas with a lot of street life and good restaurants - go to Carlebach and HaShmonaim hear the Tel Aviv Cinemateque. Tons and tons of interesting restaurants. Philippe, on Carlebach and Yehuda Ha Levi, is a pizzeria with a wood-burning oven run by a Frenchman, and has as good a pizza as you'll find in New York or anywhere else. A little further down Yehuda Ha Levy is Ruben, which has the first real deli style pastrami sandwich to appear in Israel.
Ibn Gvirol Blvd, opposite the Tel Aviv municipality, is also a fun stroll, under an arcade, with tons of places to eat (mostly street food). This is where Brasserie is.
Bograshov between Pinsker and Ben Yehuda is also a lively street lined with good restaurants (felafel gabbai on Shalom Aleichem is legendary, and the hummus place, I think it's called Chalil, on Pinsker just past Bograshov is great also). Don't miss the tiny "kurtosk" place. I think it's an Israeli invention. Somebody figured out that the crispy exterior of the coffee cake was the most delicious part, as opposed to the doughy interior, so these guys came up with a special patent for producing only the coffee cake shell. They paint the batter onto hot, rotating vertical rods. The resulting, crispy shell is quite addictive.
And then of course there's Jaffa, Neve Tzedek, Dizengoff, Florentine, Rothschild Blvd, and last but not least the resplendant downtown area with its lavishly renovated bauhaus buildings (where tapas achad aham is). In the last twenty years Tel Aviv has gone from being an ugly, dilapidated city only a mother could love into one of the great cities of the world, with restaurants to match. You're in for a treat!
Here are two worthwhile websites for Tel Aviv:
Maybe someone else can help you with Jerusalem. The last time I ate there with any frequency was two years ago. As I've posted here previously, Terra, Adom and Zuni were excellent choices back then. Terra has outdoor seating, and Adom has a beautiful courtyard.