Hi J
yes very do-able it’s only about 40miles from Tel Aviv to Jerusalem.
Bus is quickest believe it or not. Train is more comfortable but takes longer.
The old city of Jerusalem is actually quite small and all quarters could be seen, eg Christian qt including the Vila Delarosa and the church of the sepulchre, western wall, Muslim quarter including the market streets in 2-3 hours comfortably.
Taxis will also take you for a fixed price, wait and then bring you back....but most expensive option.
rob