Tel Aviv or Jerusalem?

Jerusalem.
And then let us know how much time you have, and what your interests are on the trip, and then we can think about other suggestions.
And yep, you asked for experiences and I've got some, maybe later in the post.

We give better advice if we know more about your interests and objectives for the trip.

And Chani is a regular contributor here, she's Israeli, she'll be helpful but she's probably asleep right now.

Good advice in the post above, IMHO.
You can also stay, sometimes, in monasteries or convents, some in the Old City, or one used to be able to. But not during a pilgrimage time.

I'm awake now :-)

Home base implies you want see more than one city, using day trips. The only reasonable day trip from Jerusalem is to the Dead Sea. OTOH there's a whole lot to explore in J'lem. Tel Aviv has great beaches, nightlife and a few interesting sights. It's possible to day trip by train to Haifa and Akko and other lesser-known towns that are worth a few hours, and to Caesarea with a taxi to/from the train station. There are good hotels at many budget levels in both cities.

You can get 1-3 day big bus tours, but they have all the disadvantages of big bus tours.

Jerusalem by far, it is one of the most amazing cities in the World. You can see much of the city without a tour or guide, but have a guide book and research what to see prior to your trip.

Tel Aviv is Traffic Central. You will need to get on the road early and come home late to avoid hours in a six lane parking lot.
That said, its a great city once your there. I like Herzliya its a great beach town with HWY access to move all about the country.
When you drive into Jerusalem just park in the Mall Parking lot by the old city (Jaffa Gate I believe).
Nice condos to rent in Herzliya also. Check out the Marina also.

I believe there's an old off-color joke, perhaps from Borscht Belt days, involving a business traveler who checks into a hotel in Jerusalem. He asks the desk clerk about where to find some "entertainment." He isn't specific, but in the course of the long, wordy joke, it become clear that he means personal-service entertainment. The desk clerk finally understands, and says, "Ooooooh! Well, ... she [emphaized to mean, one person only] moved to Tel Aviv."

It wouldn't be understood in Israel (not sure I get it either).

My favorite tourist joke: An American gets in a taxi in Jerusalem, asks for the Wailing Wall (Israelis never call it that). The driver doesn't understand, so the American says he wants to go where all the Jews go to cry. The driver nods understandingly and drives him to the Income Tax office.

Ok, Jerusalem it is! We are interested in all the majors sites, by walking, and taking tours. I will have my guide book I hand, and of course a city map. Would like imput on arriving, and the best way to get into the city. Also cost, concerned about having the correct amount of cash, to pay a driver? Taxi? Of course would like to stay near the old part of the city, and not have to break the bank. Any suggestions besides the King David? Way too expensive. Any favorite tour guide, or tour company? Thanks so much for your expertise!!

My husband and I are travelers. We have a love affair with Europe. But, now is the trip of a lifetime, Israel. We go with a open agenda, and will treasure each experience. We are Christian, and visiting sites significant to the life and teaching of Jesus, but would also like to experience other faiths. I am very interested in the Yad Vashem Holocaust History Museum. I would like to travel by public or private transportation. We are looking to travel the first week in March. Again, Thank you for all the imput.

I can recommend the Jerusalem Hotel, not far from the Damascus Gate. (on Antara Ben Shadad St.) It is a beautiful place, a former Arab mansion. We loved it and the people who own it. I am now remembering that several Christian clergymen were staying there which may or may not mean it is convenient to Christian sites.

Jerusalem.

Don't let people knock taking a tour. I took two day long tours: one a walking tour of the old city and the other a day long trip to Masada and the Dead Sea. Both were very good.

I took them through Rent a Guide.

Also be aware that starting Friday night through Saturday night, everything shuts down....businesses, public transit, restaurants. Some restaurants will be open and your hotel will know which ones. That's probably a good day to go to Gallilee/Bethlehem/etc.

I went for a short trip to Israel two summers ago. We stayed in Tel Aviv (Embassy Hotel), which was a good choice for us. We were able to go to the beach (only about a five minute walk) and also walked to and explored Old Town Jaffa. We booked three different group day tours with Bein Harim tour groups: Nazareth & Sea of Galilee; Jerusalem & Bethlehem; and Masada & Dead Sea. For our purposes, these tours worked well for my two friends and I. We were fairly pleased with the organized tours, although they did force the obligatory shopping stops, but that seems to be fairly common. If I ever go back to Israel again, I would hope to go with a church based tour, but at least on this trip I got to see some important Christian sites that I will never forget.