Hi Cynthia. Since you'll be in Haifa and have at least a little opportunity to see its sights, you should head somewhere else for the rest of your time. So I'll start with transportation. Trains and most buses stop running on Friday afternoon, 2-3 hours before sunset at 5.45 and resume 2-3 hours after sunset on Saturday. Taxis are readily available. For travel to other cities, you can also take a "sherut", a shared taxi, from a central point in one city to a central point in another city. That is a much less expensive option than a taxi. You can take the #940 bus from Haifa to Jerusalem. The ride takes 2 hours, and there are buses about once an hour from early morning till 8.30 pm. So you could get to Jerusalem as early as Thursday night. Or you could take the train from Haifa to Tel Aviv. The ride takes about 1 hour and there's at least one train an hour 24 hours a day (until Friday afternoon). Between TA and J-m, the bus is about a 1 hour ride (according to the schedule, but it's probably more if you hit rush hour traffic on Sunday). So you could go to TA for a day, then spend the next 2 days in J-m. Or go to J-m and end in TA. It's about 20 minutes faster to get to the airport from TA than from J-m by taxi and a lot cheaper - but that depends on your budget. There is a cheaper way to go to the airport from J-m, using a shared taxi but that can add as much as an hour to your travel time.
How much you can see depends on whether you need to spend Thursday night in Haifa and when your flight out is - Sunday night or Monday morning. With that info, I can give you more suggestions and advice.
This time of year, I'd probably want to spend all 3 days in Jerusalem - the beach is not a big draw, but you could go to TA on Saturday night and day trip to Caesarea by train & taxi, then visit the ancient port of Jaffa in the late afternoon/early evening. J-m has plenty to occupy you for 3 full days. The Old City alone can fill up a day or two. You can take a this day trip to the Dead Sea & Masada - I recommend it even though it's not guided tour because it's easy to see the places on your own - get the audio guide at Masada, Ein Gedi is a nature hike and the Dead Sea is bathing. It's all you need. If you decide to take a dip in the Dead Sea (water will be chilly but not icy), let me know and I'll give you some very important tips. There's plenty more to see and do in J-m.
If you don't want to share specifics on the forum, you can PM me.