Sylvia's advice is good - the "sherut" is a shared taxi so the price is decent, and you don't have to wait for the bus. Typically the sherut will stop in the Central Bus Station and one or two locations at the destination, they're not a door-to-door service. Let the driver know where you're going and he can drop you off at his closest stop. In the cities, the taxis need to run a meter, and almost everyone speaks English, so if you get the feeling that someone is screwing with you, they probably are, so feel free to straighten them out. A few hand gestures with some yelling will either fix things or get you in a fight
Since the security issue came up, I'll give you the ground rules we use when we go. All the cities are really safe, I let the kids hang out with their friends and relatives until pretty late. Petty crime is really not an issue. City buses are a no-no, we use taxi service. We typically spend time in the Old City, but are aware of what's going on. That's just us, and everybody has their own, so go with what you feel comfortable with.
The King David is a great hotel but expensive, so I'd look for some alternatives, and Thumper's advice about being in the central area is sound. I don't think I've ever stayed in a hotel in J'lem so I can't help with specifics. If you have time for sightseeing outside the city, Masada is a must. An evening departure to see the sound and light show at night and a dawn climb is one option, or you can just do a day trip. It's hot there (daytime) all year, so plan and dress accordingly. This may be one of the only times I would recommend an organized tour as opposed to DIY. Tel-Aviv is a great city, but there are other places I would go before that. Maybe the last night is worth staying there (along the beachfront there are half a dozen or so hotels, including a Sheraton, HI, and I think a Hilton but it's a bit out of the way). The old city of Jaffa (Yaffo) is really nice also for a seafood dinner and some romantic strolling along the waterfront.
Now for the important stuff - you have to try some real falafel, and ask someone to recommend a local place that serves "salads and shipudim", basically skewers of meat along with a dozen or so different appetizer type salads. That's the first thing I do whenever I go back. The fruits and vegetables are simply among the best in the world, and because the country has 2 growing seasons, most things are in season all the time (apples and oranges excluded).
By now I'm ready to buy a ticket and just go for a few days!