That's kind of a difficult needle to thread. Banias and Tel Dan are close to the northern border of Israel, while Jerusalem is in the center. We're a small country, but if you base yourself in one place, that's still a lot of driving. I can recommend a tour guide that provides transportation, but that might not completely resolve the issue of schlepping luggage.
Maybe the best compromise is to stay up north a few days and stay in Jerusalem a few days.
I have had wonderful experiences at a number of moderately priced hotels / accommodation up north and in Jerusalem, including:
Ohalo Manor - On the southwestern shore of the Sea of Galilee, within walking distance from the Yardenit Baptismal Site on the Jordan River. Not cheap, but tremendous value for a fantastic place in a great location.
Vered HaGalil - Also a little more expensive than I usually spend on accommodation, but also well worth it. On a farm, they offer cabins overlooking the northern Sea of Galilee. It was pretty amazing to wake up with horses grazing a few feet from the cabin and watch the sun come up over the Golan Heights to the east. Great outdoor pool, too.
Dona Gracia - In Tiberias, it's a hotel and museum dedicated to an extraordinary Jewish woman I had never heard of growing up, including seven years in Jewish day schools and a lot of Jewish history education. Incredibly interesting, although not a five-star hotel by any means.
Rimonim Nazareth - Appears to be closed right now. Decent location, within walking distance of the Old City and Mary's / Miriam's Well. A little expensive for the quality of hotel. However, I was there for only one night in 2015; it might be better now.
Israel Youth Hostel Association Beit She'an / Rabin Guest House in Jerusalem - I have stayed in a number of the IYHA hostels and I enjoy their consistent high-quality, no-frills accommodation.
HaPa'amonim Studios - I believe there are two HaPa'monim properties; one is a hotel and the other offers apartments. I stayed in an apartment, which is in a building without an elevator, so unless you get a ground-floor apartment, it might not good for you. Right on King George Street downtown, so great location. I stayed there last year for Israel's Independence Day. Perfect.
Hotel La Perle - Location, location, location. Right off of Ben Yehuda, King George, and Yaffo streets downtown. I stayed in a tiny, functional single room. I don't think they have any rooms on the ground floor, and I don't remember there being an elevator. I stayed there for Israel's Independence Day a few years ago. Fun.
ibis Styles Jerusalem - There are now three ibis properties in Jerusalem - maybe four. I haven't stayed here, but when I stayed at La Perle around the corner, the ibis Styles on Ben-Yehuda Street had a 1+1 Happy Hour in their ninth-floor bar / dining room with terrace. That was awesome.
Little House in Baka - On Derekh Hebron, not downtown, a charming bed and breakfast in a charming neighborhood. Wonderful promenades with breathtaking views of the Old City within walking distance.
National Hotel East Jerusalem - A couple of blocks from Nablus Gate, a decent hotel with a rooftop dining room.
Shalom Hotel Jerusalem (former Rimonim Jerusalem) - A decent hotel in Bayit Vegan, so not downtown. Compared to the other places I have stayed, their locations, and their prices, I would not recommend this hotel - unless they have improved since I stayed there in 2015.
In a couple of weeks, I will be staying at Beit Nofesh (Vacation Home) Weiss in Beit Hillel near Kiryat Shmona; the Jordan Valley Birding Lodge in Kfar Ruppin near Beit She'an; and at the Kaplan Hotel in downtown Jerusalem. Unfortunately, all I can write about them is that they look great and are reasonably priced for the week before and during Israel's Memorial and Independence days...